{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Nanostructures out of equilibrium with KWANT\n", "\n", "### © Marko Petrović, University of Delaware\n", "[PHYS824: Nanophysics & Nanotechnology](https://wiki.physics.udel.edu/phys824) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is covered in this notebook\n", "- Two terminal Landauer-Buttiker formula\n", " - Square lattice (spinless) with temperature smearing.\n", " - Square lattice with Rashba interaction.\n", " - Square lattice with disorder and transmission matrix eigenvalues.\n", " - Ring with AB oscillations.\n", "- Buttiker dephasing (to be added).\n", "- Spin Hall effect in four terminal device.\n", "- Topological Hall effect in four terminal device. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.1 Conductance in a two-terminal square ribbon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we need to create a two-terminal ribbon on a square lattice." ] }, { "cell_type": "code", "execution_count": 594, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import kwant\n", "import matplotlib.pyplot\n", "\n", "\n", "def lead_along_x(pos):\n", " x, y = pos\n", " width = 3.5\n", " return abs(y) < 0.5*width \n", "\n", "def system_shape(pos):\n", " x, y = pos\n", " width = 3.5\n", " length = 20.0\n", " return abs(x) < 0.5*length and abs(y) < 0.5*width\n", "\n", "# Build the system\n", "sys = kwant.Builder()\n", "lat = kwant.lattice.square(norbs=1)\n", "\n", "v1, v2 = lat.prim_vecs\n", "t = 1. # Hopping energy\n", "\n", "left_direction = kwant.TranslationalSymmetry(-v1)\n", "lead_left = kwant.Builder(left_direction)\n", "\n", "# Create main scattering region\n", "sys[lat.shape(system_shape, (0, 0))] = 0.0\n", "sys[lat.neighbors()] = -t\n", "\n", "# Create left lead\n", "lead_left[lat.shape(lead_along_x, (0, 0))] = 0.0 \n", "lead_left[lat.neighbors()] = -t\n", "\n", "sys.attach_lead(lead_left)\n", "sys.attach_lead(lead_left.reversed())\n", "\n", "sys_f = sys.finalized() # Create finalized sytem\n", "kwant.plot(sys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1.1 Transmission and scattering matrix\n", "\n", "To calculate transmission in a two-terminal device, use kwant.smatrix object to obtain the scattering matrix at a given energy. The obtained scattering matrix object has a method called transmission which is used to calculate transmission between any pair of the attached leads." ] }, { "cell_type": "code", "execution_count": 603, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "t10 = [] # Transmission from lead 0 to lead 1\n", "energies = np.linspace(-5, 5, 200)\n", "\n", "for energy in energies:\n", " smatrix = kwant.smatrix(sys_f, energy)\n", "\n", " # Here, we calculate the transmission \n", " # from the first lead (left lead) \n", " # to the second lead (right lead). \n", " # Indexing starts at zero, and it\n", " # depends on the order in which \n", " # the leads were attached. Lead\n", " # which is attached first will get \n", " # the index zero, the one that is\n", " # attached second will get the index\n", " # one etc.\n", " \n", " # The transmission function is T(E) = Tr[t*t^\\dagger]\n", " # Transmission from the lead 0 to lead 1\n", " t10.append(smatrix.transmission(1, 0))\n", "\n", "t10 = np.array(t10)\n", "plt.figure(dpi=100)\n", "plt.plot(energies, t10, color='C0');\n", "plt.xlabel('Fermi Energy (eV)', fontsize=12);\n", "plt.title('Zero-temperature conductance in a two-terminal device', fontsize=12)\n", "plt.ylabel(r'G ($\\frac{2e^2}{h}$)', fontsize=12);\n", "plt.xlim(-5, 5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1.2 Temperature smearing of the conductance\n", "\n", "Temperature smearing is performed by convolution \n", "$$ G(T, E_F) = \\frac{2e^2}{h}\\int_{-\\infty}^{+\\infty} T(E)\n", "\\left(-\\frac{\\partial f(E)}{\\partial E}\\right) dE $$ \n", "with a derivative of the Fermi-Dirac function\n", " $$ -\\frac{\\partial f(E)}{\\partial E} = \n", " \\frac{1}{4k_BT}{\\rm sech}^2\\left(\\frac{E-E_{\\rm F}}{2k_BT}\\right)$$" ] }, { "cell_type": "code", "execution_count": 604, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SUM = 0.9998857350102481\n", "8Kb*T = 0.206808\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "KB = 8.617e-5 # eV / K\n", "\n", "def F(energy, ef=0, temp=300.):\n", " n = 1.0 / (4 * KB * temp)\n", " return n * (1.0 / np.cosh((energy - ef) / (2*KB*temp)))**2\n", "\n", "ens = np.linspace(-0.25, 0.25, 100)\n", "plt.figure(dpi=100)\n", "de = ens[1] - ens[0]\n", "plt.plot(ens, F(ens)*de);\n", "print('SUM = ', (F(ens)*de).sum())\n", "print(\"8Kb*T =\", 8*KB*300)\n", "plt.xlabel('Energy (eV)', fontsize=12);\n", "plt.ylabel(r'$-\\frac{\\partial f(E)}{\\partial E}$', fontsize=12);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we convolute the previously computed conductance with temperature." ] }, { "cell_type": "code", "execution_count": 605, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Compute transmission close to\n", "# one of the steps\n", "t10 = [] \n", "energies = np.linspace(-4, 4, 300)\n", "for energy in energies:\n", " smatrix = kwant.smatrix(sys_f, energy)\n", " t10.append(smatrix.transmission(1, 0))\n", "t10 = np.array(t10)\n", "\n", "\n", "t_conv = []\n", "temperature = 300.\n", "de = energies[1] - energies[0]\n", "for ef in energies:\n", " df = F(energies, ef=ef, temp=temperature)\n", " t_conv.append((df*t10*de).sum())\n", "\n", "t_conv = np.array(t_conv)\n", "plt.figure(dpi=150, figsize=(3, 3)) # Set figure size in inches\n", "plt.plot(energies, t10, color='gray', lw=1.0, label=r'T = 0 K');\n", "plt.plot(energies, t_conv, color='C3', lw=1.0, label=r'T = 300 K');\n", "plt.legend();\n", "plt.xlim(-4, 4);\n", "plt.xlabel('Fermi Energy (eV)')\n", "plt.ylabel(r'G $(\\frac{2e^2}{h}$)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.2 Rashba spin-orbit coupling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Rashba Hamiltonian on the square tight-binding lattice of sites ${\\bf m} = (m_x, m_y)$ is given by\n", "\n", "\n", "$$\n", "\\hat{H}=\\sum_{{\\bf m}\\sigma} \\varepsilon_{\\bf m} \n", "|{\\bf m}\\sigma\\rangle\\langle{\\bf m}\\sigma|+\n", "\\sum_{{\\bf mm'}\n", "\\sigma\\sigma'} \n", "t_{\\bf mm'}^{\\sigma\\sigma'}\n", "|{{\\bf m}\\sigma}\\rangle \n", "\\langle{{\\bf m'}\\sigma'}|.\n", "$$\n", " \n", " Its hopping parameters are non-trivial $2 \\times 2$ Hermitian matrices ${\\bf t}_{\\bf m'm}=({\\bf t}_{\\bf mm'})^\\dagger$ in the spin space\n", "\n", "$$\n", "{\\bf t}_{\\bf mm'}=\\left\\{\n", "\\begin{array}{cc}\n", "-t{\\bf I}_{\\rm 2}-it_{\\rm SO}\\hat{\\sigma}_y &\n", "({\\bf m}={\\bf m}'+{\\bf e}_x)\\\\\n", "-t{\\bf I}_{\\rm 2}+it_{\\rm SO}\\hat{\\sigma}_x & ({\\bf m}={\\bf m}'+{\\bf e}_y)\n", "\\end{array}\\right.,\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we need to define unit matrix $I_2$ and Pauli matrices\n", "\n", "$I_2 = \\left(\\begin{matrix} 1 & 0 \\\\ 0 & 1\\end{matrix}\\right) $,\n", "$\\sigma_x = \\left(\\begin{matrix} 0 & 1 \\\\ 1 & 0\\end{matrix}\\right) $,\n", "$\\sigma_y = \\left(\\begin{matrix} 0 & -i \\\\ i & 0\\end{matrix}\\right) $,\n", "$\\sigma_z = \\left(\\begin{matrix} 1 & 0 \\\\ 0 & -1\\end{matrix}\\right) $" ] }, { "cell_type": "code", "execution_count": 606, "metadata": {}, "outputs": [], "source": [ "unit = np.array([[1, 0], [0, 1]])\n", "sigma_x = np.array([[0, 1], [1, 0]])\n", "sigma_y = np.array([[0, -1j], [1j, 0]])\n", "sigma_z = np.array([[1, 0], [0, -1]])" ] }, { "cell_type": "code", "execution_count": 578, "metadata": {}, "outputs": [], "source": [ "def make_rashba_system(rsoc=1.0, t=1.0, width=3., length=4.):\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return (y > 0) and (y <= width) \n", "\n", " def system_shape(pos):\n", " x, y = pos\n", " in_x = (x > 0) and (x <= length)\n", " in_y = (y > 0) and (y <= width)\n", " return in_x and in_y\n", " \n", " def rashba(site1, site2):\n", " x1, y1 = site1.pos\n", " x2, y2 = site2.pos\n", " \n", " # Check if two sites are connected\n", " # with hopping along x-direction\n", " # (Then they have the same y-coordinate)\n", " hopping_along_x = abs(y2 - y1) < 1.e-6 \n", " if hopping_along_x: \n", " hopping = -t*unit - 1j*rsoc*sigma_y\n", " else: # Set hopping along y\n", " hopping = -t*unit + 1j*rsoc*sigma_x\n", " \n", " # Notice that here hoppings are not scalars\n", " # but [2 x 2] matrices\n", " return hopping\n", "\n", " # Build the system\n", " sys = kwant.Builder()\n", " # Notice that there are now two orbitals per site\n", " lat = kwant.lattice.square(norbs=2)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " lead_left = kwant.Builder(left_direction)\n", "\n", " # Create main scattering region\n", " sys[lat.shape(system_shape, (1, 1))] = 0*unit\n", " sys[lat.neighbors()] = rashba\n", "\n", " # Create left lead\n", " lead_left[lat.shape(lead_along_x, (1, 1))] = 0*unit \n", " lead_left[lat.neighbors()] = rashba\n", "\n", " sys.attach_lead(lead_left)\n", " sys.attach_lead(lead_left.reversed())\n", "\n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = lead_left.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "code", "execution_count": 607, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sys, lead = make_rashba_system(width=2, length=3, rsoc=1.0)\n", "kwant.plot(sys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, compute dispersion and transmission in this ribbon" ] }, { "cell_type": "code", "execution_count": 610, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t10 = [] # Transmission from lead 0 to lead 1\n", "energies = np.linspace(-5, 5, 200)\n", "\n", "for energy in energies:\n", " smatrix = kwant.smatrix(sys, energy)\n", " t10.append(smatrix.transmission(1, 0))\n", " \n", "plt.figure(dpi=100, figsize=(3, 3));\n", "kwant.plotter.bands(lead);\n", "t10 = np.array(t10)\n", "plt.plot(energies, t10, color='C0');\n", "plt.xlabel('Fermi Energy (eV)', fontsize=12);\n", "plt.title('Zero-temperature conductance in a two-terminal Rashba device',\n", " fontsize=12);\n", "plt.ylabel(r'G ($\\frac{e^2}{h}$)', fontsize=12);\n", "plt.xlim(-5, 5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.3 Introducing Anderson disorder" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Anderson Hamiltonian on the square tight-binding lattice \n", "of sites ${\\bf m} = (m_x, m_y)$ is given by\n", "\n", "$$\n", "\\hat{H}=\\sum_{{\\bf m}} \\varepsilon_{\\bf m} \n", "|{\\bf m}\\rangle\\langle{\\bf m}|+\n", "\\sum_{{\\bf mm'}} \n", "t_{\\bf mm'}\n", "|{{\\bf m}}\\rangle \n", "\\langle{{\\bf m'}}|.\n", "$$\n", "\n", "The on-site potential is a uniform random variable\n", "$\\varepsilon_{\\bf m} \\in [-W/2,W/2]$ modeling short range isotropic scattering." ] }, { "cell_type": "code", "execution_count": 548, "metadata": {}, "outputs": [], "source": [ "def make_system(w=5, t=-1.0, width=3, length=4):\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return (y > 0) and (y <= width) \n", "\n", " def system_shape(pos):\n", " x, y = pos\n", " in_x = (x > 0) and (x <= length)\n", " in_y = (y > 0) and (y <= width)\n", " return in_x and in_y\n", " \n", " def random_potential(site):\n", " pot = np.random.random()\n", " pot_w = w*(2*pot - 1)/2. \n", " return pot_w\n", " \n", " sys = kwant.Builder()\n", " lat = kwant.lattice.square(norbs=1)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " lead_left = kwant.Builder(left_direction)\n", "\n", " # Create main scattering region\n", " sys[lat.shape(system_shape, (1, 1))] = random_potential\n", " sys[lat.neighbors()] = -t\n", "\n", " # Create left lead (no potential disorder)\n", " lead_left[lat.shape(lead_along_x, (1, 1))] = 0.\n", " lead_left[lat.neighbors()] = -t\n", "\n", " sys.attach_lead(lead_left)\n", " sys.attach_lead(lead_left.reversed())\n", " \n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = lead_left.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3.2 Plot onsite potential" ] }, { "cell_type": "code", "execution_count": 612, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sys, lead = make_system(w=0.5, length=20, width=10)\n", "np.random.seed(5)\n", "h = sys.hamiltonian_submatrix()\n", "v = np.diag(h)\n", "kwant.plotter.map(sys, v.real);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3.3 Compute conductance using transmission matrix" ] }, { "cell_type": "code", "execution_count": 613, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t10 = [] # Transmission from lead 0 to lead 1\n", "energies = np.linspace(-5, 5, 100)\n", "\n", "for energy in energies:\n", " smatrix = kwant.smatrix(sys, energy)\n", " # Note, you need to set the seed\n", " # each time you call a solver\n", " np.random.seed(2) \n", " tmat = smatrix.submatrix(1, 0)\n", " tt = np.dot(tmat, tmat.conj())\n", " t10.append(np.trace(tt))\n", " \n", "plt.figure(dpi=100, figsize=(3, 3));\n", "t10 = np.array(t10)\n", "plt.plot(energies, t10, color='C0');\n", "plt.xlabel('Fermi Energy (eV)', fontsize=12);\n", "plt.title('Zero-temperature conductance in a two-terminal device', fontsize=12)\n", "plt.ylabel(r'G ($\\frac{2e^2}{h}$)', fontsize=12);\n", "plt.xlim(-5, 5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3.4 Eigenvalues of the transmission matrix" ] }, { "cell_type": "code", "execution_count": 614, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "seeds = np.arange(100) # Do the averaging over 10 distributions\n", "t_evals = []\n", "\n", "for seed in seeds:\n", " smatrix = kwant.smatrix(sys, 0.)\n", " np.random.seed(seed) \n", " tmat = smatrix.submatrix(1, 0)\n", " tt = np.dot(tmat, tmat.conj())\n", " evals = np.linalg.eigvals(tt)\n", " t_evals = t_evals + list(evals)\n", "\n", "bins = np.linspace(0, 1, 100)\n", "plt.figure(dpi=100, figsize=(3, 3));\n", "plt.hist(t_evals, bins=bins);\n", "plt.xlabel('Transmission Eigenvalue', fontsize=12);\n", "plt.ylabel('P(T)', fontsize=12);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.4 Introducing vacancy disorder" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In a similar way in which we add sites to the system, we use the delete (del) command to remove sites from the system. Notice that\n", "sites can only be removed from a system which is not finalized." ] }, { "cell_type": "code", "execution_count": 615, "metadata": {}, "outputs": [], "source": [ "def make_disordered_system(seed=0, nvac=5, t=-1.0, width=3, length=4):\n", " \"\"\"\n", " Parameters\n", " ----------\n", " seed : integer\n", " Determines how vacancies are sampled. Each\n", " integer will produce a unique distribution\n", " of vacancies\n", " nvac : integer\n", " Number of vacancies in the system\n", " \"\"\"\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return (y > 0) and (y <= width) \n", "\n", " def system_shape(pos):\n", " x, y = pos\n", " in_x = (x > 0) and (x <= length)\n", " in_y = (y > 0) and (y <= width)\n", " return in_x and in_y\n", " \n", " sys = kwant.Builder()\n", " lat = kwant.lattice.square(norbs=1)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " lead_left = kwant.Builder(left_direction)\n", "\n", " # Create main scattering region\n", " sys[lat.shape(system_shape, (1, 1))] = 0\n", " sys[lat.neighbors()] = -t\n", "\n", " # Create left lead\n", " lead_left[lat.shape(lead_along_x, (1, 1))] = 0\n", " lead_left[lat.neighbors()] = -t\n", "\n", " sys.attach_lead(lead_left)\n", " sys.attach_lead(lead_left.reversed())\n", " \n", " np.random.seed(seed)\n", " \n", " nv = 0\n", " lengths = np.arange(1, length+1)\n", " widths = np.arange(1, width+1)\n", " nv = 0 \n", " while nv < nvac:\n", " i = np.random.randint(length)+1\n", " j = np.random.randint(width)+1\n", " try:\n", " del sys[lat(i, j)]\n", " nv += 1\n", " except KeyError:\n", " continue\n", " \n", "\n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = lead_left.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "code", "execution_count": 616, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sys, lead = make_disordered_system(seed=2, length=10, width=10, nvac=3)\n", "kwant.plot(sys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.5 Aharonov-Bohm oscillations" ] }, { "cell_type": "code", "execution_count": 620, "metadata": {}, "outputs": [], "source": [ "def make_ring(t=1.0, out_radius=10, in_radius=5, width=4, length=5.):\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return abs(y) < 0.5*width\n", "\n", " def system_shape(pos):\n", " x, y = pos\n", " r = np.sqrt(x**2 + y**2)\n", " in_outer = r < out_radius \n", " in_inner = r < in_radius\n", " in_ring = in_outer and not in_inner\n", " return in_ring\n", " \n", " def bfield(site1, site2, flux):\n", " x1, y1 = site1.pos\n", " x2, y2 = site2.pos\n", " if x1 == -1 and y1 < 0 and y1 == y2: \n", " hop = -t*np.exp(-1j*flux)\n", " else:\n", " hop = -t\n", " return hop\n", " \n", " sys = kwant.Builder()\n", " lat = kwant.lattice.square(norbs=1)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " lead_left = kwant.Builder(left_direction)\n", "\n", " r_cent = 0.5*(in_radius + out_radius)\n", " sys[lat.shape(system_shape, (r_cent, 0))] = 0.0\n", " sys[lat.neighbors()] = bfield \n", "\n", " lead_left[lat.shape(lead_along_x, (0, 0))] = 0.\n", " lead_left[lat.neighbors()] = -t\n", "\n", " sys.attach_lead(lead_left)\n", " sys.attach_lead(lead_left.reversed())\n", " \n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = lead_left.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "code", "execution_count": 618, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ring_sys, lead = make_ring(in_radius=5, out_radius=13, width=10, length=20)\n", "kwant.plot(ring_sys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.5.1 Transmission at zero magnetic field" ] }, { "cell_type": "code", "execution_count": 621, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t10 = [] # Transmission from lead 0 to lead 1\n", "energies = np.linspace(-5, 5, 100)\n", "\n", "for energy in energies:\n", " smatrix = kwant.smatrix(ring_sys, energy, params={'flux':0.})\n", " t10.append(smatrix.transmission(1, 0))\n", " \n", "plt.figure(dpi=100, figsize=(3, 3));\n", "plt.plot(energies, t10, color='C0');\n", "plt.xlabel('Energy (eV)', fontsize=12);\n", "plt.title('Conductance in a two-terminal device', fontsize=12)\n", "plt.ylabel(r'G ($\\frac{2e^2}{h}$)', fontsize=12);\n", "plt.xlim(-5, 5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.5.2 Aharonov-Bohm oscillations" ] }, { "cell_type": "code", "execution_count": 460, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t10 = [] # Transmission from lead 0 to lead 1\n", "fluxes = np.linspace(0.1, 30., 100)\n", "\n", "for flux in fluxes:\n", " smatrix = kwant.smatrix(ring_sys, 3.85, params={'flux': flux})\n", " t10.append(smatrix.transmission(1, 0))\n", " \n", "plt.figure(dpi=100, figsize=(3, 3));\n", "plt.plot(fluxes/(2*np.pi), t10, color='C0');\n", "plt.xlabel('Magnetic flux', fontsize=12);\n", "plt.ylabel(r'G ($\\frac{2e^2}{h}$)', fontsize=12);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Spin Hall effect in a four-terminal device" ] }, { "cell_type": "code", "execution_count": 535, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from math import sqrt\n", "import random\n", "import itertools as it\n", "import tinyarray as ta\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import kwant\n", "from sympy import S, Eq, solve, Symbol\n", "\n", "class Honeycomb(kwant.lattice.Polyatomic):\n", " \"\"\"Honeycomb lattice with methods for dealing with hexagons\"\"\"\n", "\n", " def __init__(self, name=''):\n", " prim_vecs = [[0.5, sqrt(3)/2], [1, 0]] # bravais lattice vectors\n", " # offset the lattice so that it is symmetric around x and y axes\n", " basis_vecs = [[-0.5, -1/sqrt(12)], [-0.5, 1/sqrt(12)]]\n", " super(Honeycomb, self).__init__(prim_vecs, basis_vecs, name)\n", " self.a, self.b = self.sublattices\n", "\n", " def hexagon(self, tag):\n", " \"\"\" Get sites belonging to hexagon with the given tag.\n", " Returns sites in counter-clockwise order starting\n", " from the lower-left site.\n", " \"\"\"\n", " tag = ta.array(tag)\n", " # a-sites b-sites\n", " deltas = [(0, 0), (0, 0),\n", " (1, 0), (0, 1),\n", " (0, 1), (-1, 1)]\n", " lats = it.cycle(self.sublattices)\n", " return (lat(*(tag + delta)) for lat, delta in zip(lats, deltas))\n", "\n", " def hexagon_neighbors(self, tag, n=1):\n", " \"\"\" Get n'th nearest neighbor hoppings within the hexagon with\n", " the given tag.\n", " \"\"\"\n", " hex_sites = list(self.hexagon(tag))\n", " return ((hex_sites[(i+n)%6], hex_sites[i%6]) for i in range(6))\n", "\n", "def random_placement(builder, lattice, density):\n", " \"\"\" Randomly selects hexagon tags where adatoms can be placed.\n", " This avoids the edge case where adatoms would otherwise\n", " be placed on incomplete hexagons at the system boundaries.\n", " \"\"\"\n", " assert 0 <= density <= 1\n", " system_sites = builder.sites()\n", "\n", " def hexagon_in_system(tag):\n", " return all(site in system_sites for site in lattice.hexagon(tag))\n", "\n", " # get set of tags for sites in system (i.e. tags from only one sublattice)\n", " system_tags = (s.tag for s in system_sites if s.family == lattice.a)\n", " # only allow tags which have complete hexagons in the system\n", " valid_tags = list(filter(hexagon_in_system, system_tags))\n", " N = int(density * len(valid_tags))\n", " total_hexagons=len(valid_tags)\n", " valuef=random.sample(valid_tags, N)\n", " return valuef\n", "\n", "def cross(W, L):\n", " def shape(pos):\n", " return ((-W <= pos[0] <= W and -L <= pos[1] <= L) or # vertical\n", " (-W <= pos[1] <= W and -L <= pos[0] <= L)) # horizontal\n", " return shape\n", "\n", "## Pauli matrices ##\n", "sigma_0 = ta.array([[1, 0], [0, 1]]) # identity\n", "sigma_x = ta.array([[0, 1], [1, 0]])\n", "sigma_y = ta.array([[0, -1j], [1j, 0]])\n", "sigma_z = ta.array([[1, 0], [0, -1]])\n", "\n", "## Hamiltonian value functions ##\n", "\n", "def onsite_potential(site, params):\n", " return params['ep'] * sigma_0\n", "\n", "def potential_shift(site, params):\n", " return params['mu'] * sigma_0\n", "\n", "def kinetic(site_i, site_j, params):\n", " return -params['gamma'] * sigma_0\n", "\n", "def rashba(site_i, site_j, params):\n", " d_ij = site_j.pos - site_i.pos\n", " rashba = 1j * params['V_R'] * (sigma_x * d_ij[1] - sigma_y * d_ij[0])\n", " return rashba + kinetic(site_i, site_j, params)\n", "\n", "def spin_orbit(site_i, site_j, params):\n", " so = (1j/3.) * params['V_I'] * sigma_z\n", " return so\n", "\n", "lat = Honeycomb()\n", "pv1, pv2 = lat.prim_vecs\n", "ysym = kwant.TranslationalSymmetry(pv2 - 2*pv1) # lattice symmetry in -y direction\n", "xsym = kwant.TranslationalSymmetry(-pv2) # lattice symmetry in -x direction\n", "\n", "# adatom lattice, for visualization only\n", "adatom_lat = kwant.lattice.Monatomic(lat.prim_vecs, name='adatom')\n", "\n", "def site_size(s): \n", " return 0.25 if s.family in lat.sublattices else 0.35\n", "\n", "def site_color(s): \n", " return '#000000' if s.family in lat.sublattices else '#de962b'\n", "\n", "def create_lead_h(W, symmetry, axis=(0, 0)):\n", " lead = kwant.Builder(symmetry)\n", " lead[lat.wire(axis, W)] = 0. * sigma_0\n", " lead[lat.neighbors(1)] = kinetic\n", " return lead\n", "\n", "def create_lead_v(L,W, symmetry):\n", " axis=(0, 0)\n", " lead = kwant.Builder(symmetry)\n", " lead[lat.wire(axis, W)] = 0. * sigma_0\n", " lead[lat.neighbors(1)] = kinetic\n", " return lead\n", "\n", "def create_hall_cross(W, L, adatom_density=0.2, show_adatoms=False):\n", " ## scattering region ##\n", " sys = kwant.Builder()\n", " sys[lat.shape(cross(W, L), (0, 0))] = onsite_potential\n", " sys[lat.neighbors(1)] = kinetic\n", "\n", " adatoms = random_placement(sys, lat, adatom_density)\n", "\n", " sys[(lat.hexagon(a) for a in adatoms)] = potential_shift\n", " sys[(lat.hexagon_neighbors(a, 1) for a in adatoms)] = rashba\n", " sys[(lat.hexagon_neighbors(a, 2) for a in adatoms)] = spin_orbit\n", " if show_adatoms:\n", " # no hoppings are added so these won't affect the dynamics; purely cosmetic\n", " sys[(adatom_lat(*a) for a in adatoms)] = 0\n", " ## leads ##\n", " leads = [create_lead_h(W, xsym)]\n", " leads += [create_lead_v(L,W, ysym)]\n", " leads += [lead.reversed() for lead in leads] # right and bottom leads\n", " for lead in leads:\n", " sys.attach_lead(lead)\n", " return sys\n", "\n", "def plot_ldos(sys, Es, params):\n", " fsys = sys.finalized()\n", " ldos = kwant.ldos(fsys, energy=Es, args=(params,))\n", " ldos = ldos[::2] + ldos[1::2] # sum spins\n", " kwant.plotter.map(fsys, ldos, vmax=0.1)\n", "\n", "def plot_conductance(sys, energies,lead_i,lead_j, params):\n", " fsys = sys.finalized()\n", " data = []\n", "\n", " for energy in energies:\n", " smatrix = kwant.greens_function(fsys, energy, args=(params,))\n", " data.append(smatrix.transmission(lead_i,lead_j))\n", "\n", " plt.figure()\n", " plt.plot(energies, data)\n", " plt.xlabel(\"energy (t)\")\n", " plt.ylabel(r'Conductance ($e^2/h$)')\n", " plt.show()\n", "\n", "def plot_spin_conductance(sys, energies,lead_i,lead_j, params):\n", " fsys = sys.finalized()\n", " data = []\n", "\n", " for energy in energies:\n", " smatrix = kwant.greens_function(fsys, energy, args=(params,))\n", " ttdagger = smatrix._a_ttdagger_a_inv(lead_i, lead_j)\n", " sigma_z_matrix = np.kron(np.eye(int(len(ttdagger)/2)),sigma_z) \n", " data.append(np.trace(sigma_z_matrix.dot(ttdagger)).real)\n", " plt.figure()\n", " plt.plot(energies, data)\n", " plt.xlabel(\"energy (t)\")\n", " plt.ylabel(r'Spin conductance ($e^2/h$)')\n", " plt.show()\n", "\n", "def solvematrix4(G,I0,I2,V1,V3):\n", " # I=GxV\n", " I1,I3,V0,V2=S('I1 I3 V0 V2'.split())\n", " equations = [Eq(I0, G[0][0]*V0+G[0][1]*V1+G[0][2]*V2+G[0][3]*V3), \\\n", " Eq(I1, G[1][0]*V0+G[1][1]*V1+G[1][2]*V2+G[1][3]*V3), \\\n", " Eq(I2, G[2][0]*V0+G[2][1]*V1+G[2][2]*V2+G[2][3]*V3), \\\n", " Eq(I3, G[3][0]*V0+G[3][1]*V1+G[3][2]*V2+G[3][3]*V3)]\n", " return solve(equations, [I1,I3,V0,V2], set=True, dict=False, rational=None, manual=True, minimal=True, particular=True, implicit=False, quick=True)\n", "\n", "def plot_SH_angle(sys, energies, params):\n", " fsys = sys.finalized()\n", " data = []\n", "\n", " I0=0\n", " I2=0\n", " V1=1.0\n", " V3=0\n", "\n", " for energy in energies:\n", " smatrix = kwant.greens_function(fsys, energy, args=(params,))\n", " G=np.zeros((4,4))\n", " for i in range(4):\n", " a=0\n", " for j in range(4):\n", " G[i,j]=smatrix.transmission(i, j)\n", " if i != j: a+=G[i,j]\n", " G[i,i]=-a\n", " a=solvematrix4(G,I0,I2,V1,V3)[1]\n", " result=list(a)\n", "\n", " I1=result[0][0]\n", " I3=result[0][1]\n", " V0=result[0][2]\n", " V2=result[0][3]\n", " print(I1,I3,V0,V2)\n", "\n", " Gspin=np.zeros((4,4))\n", " for i in range(4):\n", " a=0\n", " for j in range(4):\n", " ttdagger = smatrix._a_ttdagger_a_inv(i, j)\n", " sigma_z_matrix = np.kron(np.eye(int(len(ttdagger)/2)),sigma_z) \n", " Gspin[i,j]=np.trace(sigma_z_matrix.dot(ttdagger)).real\n", " if i != j: a+=Gspin[i,j]\n", " Gspin[i,i]=-a\n", "\n", " IS0=Gspin[1,0]*(V1-V0)+Gspin[2,0]*(V2-V0)+Gspin[3,0]*(V3-V0)\n", " data.append(IS0/I1)\n", "\n", " plt.figure()\n", " plt.plot(energies, data)\n", " plt.xlabel(\"energy (t)\")\n", " plt.ylabel(\"spin hall angle\")\n", " plt.show()\n", "\n", "if __name__ == '__main__':\n", " params = dict(gamma=1., ep=0, mu=0.1, V_I=0.007, V_R=0.0165) # Au adatoms\n", "\n", " W=16\n", " L=32\n", " # W=8\n", " # L=16\n", " adatom_density=0.15\n", "\n", " sys = create_hall_cross(W, L, adatom_density, show_adatoms=True)\n", " kwant.plot(sys, site_color=site_color, site_size=site_size)\n", "\n", " sys = create_hall_cross(W, L, adatom_density, show_adatoms=False)\n", " plot_ldos(sys, 1e-5, params)\n", " \n", " Es = np.linspace(-0.1, 0.1, 100)\n", " plot_spin_conductance(sys, Es, 1, 0, params) # T01\n", " plot_conductance(sys, Es, 1, 0, params) # TS01\n", "\n", " # plot_SH_angle(sys, Es, params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3. Topological Hall effect in a four-terminal device." ] }, { "cell_type": "code", "execution_count": 536, "metadata": {}, "outputs": [ { "data": { "image/png": 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37CsxXHT54qYclqv4p8An//ZKhrLj87UtefrzLvfuL7F12OLlXpMfHaxwYMLm5t1FJivea8Ze57TDw21lXjiY/Uk8Csc83pKePnjo/0op9duapn0FeFkptTp4fU5v/5Po6Wcfy5cvP+K14x1vps1PY9tTtv7vtV2+fPmbOufrPX6sq/eapl0ePOB/FbzUCGRmfWTeiV7jjRzjRZsvvtjNv17TwH+uzXL378PfPtzO/3t7PQ+2lnj/GSlaJm0WpiNoGoyVPC5ZFOelHoPfu7CW72zP8/3fgT++r5XPv6eJb2zN82eX1PH0oQrvWJagL+eSjmnUxXUOZR2uW57kiYNl/vKyOr68Oc9tH4Y/f6CNT76zke/vKvC759fwap/JBQtiTFVk9X5JbZS94xa/sCrFDw+U+fur6vnv9Vnu/D34q4fa+OerG7h7f4lfPSvFzlGb0+qjWJ4iZ/q8bV6M9QMmv3lumlt2F/n3axv4xKtZ7vw9xcce7eBvrqjjkfYK15+epGPKpjkVIRaBoYLH5YvjPN9t8EcX1fLNbXl+8LvwJ/e18tnrm7hxe54/vqiO57srXLEkwVDBJR6RVe2OaYd3n5bk0fYyf3VFHV/YmOf2j8BfPNDGJ65r4JY9RX7r3Bo2DJi8bZ7sUtieYkV9lJ2jFr9yVpq79hX5x6sb+FTgk795qI1/eEcDP2wp8YurUuwds1laF8FTMFXxOH9+nFf7DX7n/Bq+t7PIdz+k+OP72vji+5r46uY8H72sjicOVrhuRYKujEt9QiMV1enLO1y1NMEzhwz+5JJavr41zy2/C396fyv//e4mvrOjwO9fWMPLPSaXLIozVnLRNY0FaZ2WSYf3rUzyYGuZv72yns9uyHLH78FfPtjGx69t4Pa9RX79nBq2DJmc2RSjZPtUHMUZjVG2Dlt88Jw0t+8t8q9Xz8Te/324jb97e8NM7E3YvG35PP74x/zQv9Zxwj29pmk3BA/9I0FPfwtwi1Jqd9DTf0Ap9fHw8z+Jnr6jd5iGpE7O9DnvjGW09w7TmNQpWD61cVl1jwar966vSEY1SraiPnFkm7zp05DUKdo+6ais9upokpvhygpwwVY0HKNtfUJW6hNRDc8HhewcyIr4zPmPaGv51MXlc3Fdwwd8XxGPalRsRV1wvcajtC1aPum4huXKPFIHbF9W1n8sOC2f+rgmK/BRDd8HH7G7chycoU+MWTsqri/3q3wMW0PcIU7bVeizcKajr+2ThqROyfZJRjVcX+ImqoPpKmqP45MjcCrZdXi9OE1XsXzpEs5cedqP7RmAH+OcPuzlD3s5BzQHvzcC0ydyjTd6TJUdHmkv4/mKO/bJKumDrSUKls/z3RUGCx5bhmRVunXSZtOgxVDB47muCkXL58HWEgB37Cvi+opH2stMGx6rewx6cy7bhy32jtt0TjusGzAZK3k81VnBcHx+eEDa3rO/iOUqftRZZqLi82qfrPDuGbPYNWrTnXVZ02swWfF4/GAZx1PcFdh6f0uJsu3z7CFZMd84YNI+5XBgXFb/B/IuL/YY5ExZ4feV4PSV4uG2EnnT54UeWanfOmzRMmHTNmWzccBkuOjxzKEKJdvn/gDnnfuKOJ7isY4yUxWPV3oNenIuO0dsdo9ZHJp2WNtvMl72ePJgGdNV3HNAbL33QAnD9XnyYIXxssfaflmx3zNusXPEpifnsrrXYLri8WhHGcdX3BngfKC1RNH2ea6rwnDRY/OgRdukzYEJmy1DFoN5lxe6ZUflobYSKtid8JT4JGvKKnp/TnDuH7fpmHbYMGAyUhKcZcfnvhbBedf+IranePxgmcmyx5o+k+6sy65Ri91jFl0Zh1f7TCbKHk8cLGN5irv3i60/bClRcWQHZ7TksX7A5OCUw75x2anoy7u83GOQNbzjxt7mIYvdw6WfxKNwzONEh/erNE1bNev3y4GHgCvD14A5Xwr9/f189KPyBfTBD36QD37wgydowtyjMRXlvSuTRHSNXzsrDcD7z0hRG9e4elmSRTURkhGNZFR6laW1ioakzjXLk9TENd5/RgqAXzsrTVTXeO/KJI0JnSuXJpiX0mlI6ER02ddtTurMS0d454oEyajGL54pbX/pzDSJqMa7ViRpTupcviROQ0JnYY3sX6eiGrWxBE1JnXefliQW0fiVwNYPrEqRjmlcuzzB/JoIF+txamKSked4kuX2jmUJ6hIa71uZRNc0fvWsNLqm8b6VKWoTGu9YmmBBjU46phOPyOryopoITckI1y5PkI5pfCDA+atnpYlFNK4/PUljUufKJQmaUjqNSR1dk8zDxqTOvFSEd52WJBnV+KVVYusvrkqRjGi867QE81IRLlscpy6h43iyf52OaaSiCRqSOu85PUlMF1sBbjgjRU1M45rlSRamI8QWQiqmoxRYnuyXv2NZktq4xvtXptA0jV89O01E03jv6Unq4zpXLUswP6VTG9eJRWTVfn5apzkV4brlCdJRjV9YJTh/5cw08YjG9aclaUzpXLE4TmNSZ35K+r1EVKMuodOUEp8kIhq/fOYMzlRU47oVCeanI1y6KE5tXMf1JaegJq4RjySoT+jV2PvV14i90xek3tKYf6PHCT30SqlHATRN+yjSqxMM668MhvY5pdTu2W1OP/3040tg27aQE+bPh7vvht/5Hb6zZZhfuaiZZ9szvGtVPS1jFZbVxzEcH8P1WVYfp2Wswllpg9ZJh5WNUXaPWVx/IbRM2iyri3Ao45CMaAwUXBoSuqSGmz6naVE6px0WpnVaJmzefQHsHrM4szlK66SkpXZnHXQkLTYe0UjHJPsrHtXomHJYWhdl77i03TtucUZjlI5ph6akTm/OZUW9pPD6CppT8lptXKd9yuH0hhlb94/brKiPcnDaoSauM5B3mZ+WjLyKo1haKziakjqtkzarmiRD7/oLFC2TNkuC92ORGCNFyVSL6hrThkdE0+jMuCyqjbB/Ns6mKG2TDvMDnKuIkQk+XxvXGC5KOm/HlMOyuij7xm2uvxD2TdisbIzSMeXQkBBMS+siVByF46nq+eoTOm2TDitn4TwwYbO8XjITU1GN/rxHc0rhKyhaPsvrI3RlHOandQ5M2rxTKXaPWZzdHKV10mZxrbwfmRdjrOSRimnEIxqTFckkPDjtsLg2yv7AJ3vGLVY1RWmfcpiXitCTczm9IUrO9NE0qE/oDBZkvaZ9ymFFg6y7XH8h7Bu3Oa1BfFIf1+nLuyyqkbRqy1MsrBGcjUl9Tuy950JomTgy9vLWKMMFm2zF5cz5SXYMlLjhnEYe3z/FH165iNu2jvJnVy3mob2T/OWli2natgkuu0y4H4nECdNy35I0XKXUrcCth/395g/HEUJDJiPcaKAeg8mJMeKOTW7aAsOlonQcHzxPUfR0dMsjVhtjQVpHB5bURgBYmI4Q1TXmpXSSUY2GhE5NXEMDfKWTjMh7EV1jYY20WVIbQQcWpHWiEWhKRkjGNOoTOjFdIxHRaExIttz8dISIBouDtotro+g6zE9FiEdlMSwV1VBKQyE9fVNSeuEFaelRQ1sX1UaI6DA/Lb1CQ0InHQR0VJf1h+ak2LCwJoKuaSypjaBp8nc0otEc4KxPyHUjGri+TiIqOKNBzx/i1DRYUKMT16E5FSEVlYXKiC4josbkXJyLAlsX18jf89OR6qJfOqajawovWENoSspC4oIa+ZKt4qyJENXE1kRURhM1MQ2lQNd0klGd5pSkEMuia4ATWFgTkZFWSvDVJ+QcUR0aEjqJiMa8lNzH0J+LayLoGsxPy6igKamTiml4SuIgXfWJxoK0fHZxbbRqa0Sb8afYqhOLKBLeLJy6dmTs1Rw99sxCBs9WFKZLRG2HqQmLlG8BUIfB+NgoSc8iOzVBUzQqPPza2hlK7wkcPzUZeUdjIGtHffUon9OO/bcW/Kdpx7iG9hrXP8Z72mHvh69pR+VRa8FntWNep9p+lq3H+szMZ+d+aM75j4JVO+z32dhe67PHah/+8lrnOfz1Y2KffQ7tyCsd7RrV16o/j7zKnOsd5eJH8+OxjiOu+zo+f7zzz4X6+mL99Rwn50Pv+zLE933hPgODRRfPh8mKh+XK9lXJ8SlaPnnTx3AVGcPD8RUTZQ8fGCl5AIyXPFxfMVXxMcO2tqJky++mK++5vmK8LG1GSnKOibKP40HG9DAcRcHyKdo+Zccna/pYrmKy4uEp2f6Ttq6YXvawXUXWlM8XLPlXceQ125PP+ApGii4AoyUPz5dtK9NT5Cyfsq0o2j55y8d0xFYnsNVXipGSh1KKsbKH6ymmDZny5E2fku1TchQ506va6vpqlq0eSglO24eM4VFxFXlT7m0VpzeDc7QU2upWt9gsTzBVHLk/Ic6M4eF4MF6WqU3ok7Fy4BNjlk8cFdjqY7o+00bgkwDfcFHwTpQ9bF8xbXgYVX/6lIP7anqKqYrcxyrOotg6WfGwPQJbFQVLiExiq2w1TlY8fF/8ONsnkxXxZy7wZzHwp+GILY4ntvrAcDGIvfLc2Mtbrz/2xksetqeEsmsYMgJ23RN+vE5Oll00KkMZ14ULLwTg6iVJ4hHFefNj1Cd0VjZGqY3puErhelAb1zirOUY6qnHhwjgRTePKJaKactHCOMmoxtvmxWhI6pymRUlGpLtrSOg0JnTOmRcjEdW4eKEoyly5JEFE07hgQYyamMZZTbHqUDSqQTSiyTA4oXPu/BhxHS5dLG0vX5wgFtE4f0GM2oTOqsYo9QmduoQCBcmYRkSLUhOX80d1jSsCWy9ZFCcRgXPnxwVnQ5T07IW8hMY582KkYhoXLYyjBzg1TWxPxuT9xqRORJNpga7JAmB9Uufc+XESEY2LF83Cqc/F2RgMm8OFvEREhvvnzY8Rj2hctlhsvWxxgnhE49z5MerigrM2WMjzg4U8jRjpmMaFC2JE9BmfXLIwTiL0SYAzGQzvm5I69Qmdc5qFYHTRwjhagFPXxL/pqMbZzTGagqlONAJRTdZa6hM6b5sXIxGR+wlwxZIEsRBnXGNVU5TGhEwpCCjEUT1KbVzn/AUxYhGNywOcly6KE4/AefNj1M2OPV/hKqFKn9Uc4Dws9i4+VuwRxF5SYi85K/auWCyxd+FCWcRl5UrRR0ilZpSATuA4OXt625b5vG3DmjUAPHaohOEqNg5aTFU89o7Z9OVdDk27tE7ZjJQ8to9YFCyfNX0mnq94urMCwOpeg5Kt2DIsW08HJmy6sw49WYf9EzbjZY8tQyZlW/FyrwHA050VXF/xap9JzvLZPmIxXPRom7TpzDj051x2j9lMVzw2DlqYruKFbmn7XFcFy1Ws6zfJVHx2jdoMFlwOTju0TTkMFTx2jlpkTZ+1/SaOp3jmkNj6Uo9BxVFsGjSZKnvsG7fpy7l0ZVxaJ23GSh5bhy2KluKVXgNfCU5fKcFpKbYOWYyVBGdXxqE3J9tLE2WPTYMmFUfxck+A81AFx1Os7TfJmT7bRy2GCx7tUw4Hpx0G8gFOw2PDgInpKp7vEluf765guD4bBiymDI/dYzYDeZfOjOAcLnrsGLXImz6v9ps4vuLpEGevQdlRbB4ymah47Juw6c06dGcdDkzYjJVctg6blGzBpZS09ZTilV6Tgu2zbdhipOTRMmnTlXHpzbnsHbOZKotPKq7ixQDns4cq2CFOw2fniMVQ0aNj2qFjymGg4LJ71CZr+KzrN7E8xbMBzhe7jaPHXsalbXIm9vKzYi/0Zxh7m4ck9vaPB7GXk9gbO0rsPXNoJvaypi+KPqOjIsZROvHtvpOTWmtZAs4wBOzKlbT1DlHWXApB0krFDaiYalaChBMkSFg+DQn5ee7KZXT0DdOQkGSOmllJKxrgBMk55SDh5fA24blKtk8qTFrRpBe0PUkEKQZJJMdqW7b9Wck5ENPBCBNBjmFriDNMWlGAFybnHA+n7Qtt9ARwOr7MOSM6WEFyzrFwHuGTN4Az9Il5GM7E67C1itN78z5xD8NZ8zp88oZiL0gUm40zeiyfmD7nnjHX1gvqUyxxHNnJqq8XRaHU8bf8fvqotYYhmmWWBTffDMAnNkxTdnzu2ldkoODxdGeFvWM2mwdNXuk1q2SGqYrHzTsLeL7iixtzAHxne56cKYka3VmXF3qESLJjVEgwvTmXH7aUyFs+396eB+BLm3K4vuLmXQUmyx4Pt5XpmHZY02uyedBk35jNU52ScHHnviIVx+frW6TtVzfnMF3F7XuKDBddnghIGesHTNb2y5biYx1lxkout+2WpJEvbxJbb9wmRJF79pfoy7s8e8hg95hdJXh0ZVwebJWEoe/tEErtFzfm8JXiuzsKZA2PB1pKdGVcXuox2DZssWvM4tkuoRDfc6BE0fK5cdsMTsdT3LK7wHjJ49H2Mm1TDq/2GWwcNNk/bvOjTkmguX1vEcMV4gnA17bkMRyfO/YVGSoK1XX/uM3GQZNX+wzapyRRaqLsccuuAo6v+FKA89vb8hQsoRb35lye7zLYOWqxfcTixR6DrozL/a0lsqbHTdsLqACnp4TyOl3xeKi1TOe0w+oek61DJntGbZ49VKE/73L3/hIl2+ebW8XWr2zOYXuK23YXGS0Jlbp10mFdv8H6AZOWCZsnDlYYKbrcvkeSq766WWz9xtb8MWNvTa8k6jzSVmbyaLG3Y27shSSm7QEBqycbxJ7p8+0dYusXN87E3ljZhWeeES2/6ekZWbUTOE7enh5EjwxgwYJT5I4fQ9tTtp58bY/WZnk4j6+vl5+vY17/0yeXZRiiitrQAP/5n3DTTfzxD9v41LsbuGlHgQ+fX8O6AZNzmmOUgpXtc5pFturD59fw7e0F/vvdjXzspQyP/amQZ/792kbu3FfkV85Ks2fMqu5tDxddrlyS4OnOCn9+WR1f2pTj7t+HD93Zwo2/0MxnN+T4f1fW82h7mXedlqQr65AO9mrbpxzeuzLF/S0lPnZVPZ9cm+WBP4LfvbuFL7+vma9vyfOnl9TyfLfBpYviTAQrysvrI2wfsfj1c4Q08x/XNfIvqzM88ifwB/e28ul3C1nnQ+fWsHlIEn3MYBfgggUxXu41+P0La/nm1jyfe08Tf/9ihkf+RPHnD7Txr1c3cM+BEr+wKkXLhMO8tOw99+Vcrlme4PGOCn99eR2f25jj3j+A376rhW/c0MwXNuX4m8vreeJgmWuWC7EoHuzNH5iw+cCqFPfsL/FPV9fziTVZHvxj+Mg9LXzhPU3cuK3AH15cy+pegwvmx8maHqarWNkYY/OQyW+eW8P3dxb45Lsa+aeXMjz6p/CHP2zlk+9s5NY9Rf7POWm2j1isqI/i+oqJiselixI831Xhjy+p5aub89z5e4oP3dXCt39xHp9el+Mfr6rn/tYy71uZlOSgpOQzdGVc3nVagofbhDTz3+tz3PeHgvPrNzTz5U05/vKyOp4+ZPD2pXGGix4asLg2wp4xm18+K8Ude4v82zWNfHxNhof+GH7vnhY++54mbtpe4CMX1rK23+Bt82IULUXJ9jm7Oca6AZPfOb+G7xwj9u7YV+TXzkqzO4g9kFX6auxdWseXNkvs/dadLXwriL0vXDef5U8/CtdfD2ecIcP7004sb//k7elNUxYu8nlYuJDB4RHGHBvXlzmR54tsFRwpnBB+xvUVK5YtZXB4pPp39BiCDcdtM0sEIdxj9RWv73qvIdjwZmw9XtvXEqb4sdr6FuN8Iz75SePUNVm3UD/m2FuZSrIkEpEOMMzICzX1X+P46ZvTm6ZoklsWfOc7APzLuinKjs9te4oM5EUyaveYzcZBi5e6DTqmbO5rERmlb2+XedVnN+QAmZPlTZ+795fozjo8d8hg67DMq57prNCTdbhrn8zpvx7MAT+7QeZV39lRYLLicV9LmfYpm9U9BhsGTPaM2Tx+sMJgweXWPTKn//ImafuFjTKn/8GuIiNFkajaN26ztl/WH1ombB5qKzNe8vjezkJV3AHgq5tlTn/73iL9eZenDlbYOWqzecjihS6DzmmHew+UyBge39omc/rPbpA5/Y3bZE5/9/4ShzIOL3QZbB6y2DEi6w+9OYc79hYpWj5f3TKD0/FkPWC8LJJYrZM2q3tN1vWb7B2zeKyjzHDB5Qe7ZU7/xWBe/qVNOQxHJKmGCy6Pd1TYM2axYcBkda9J26TNA61CcLlph8zpQ598fYvM6e/cJ6IXz3RW2D5is2XY4rlDBl0Zh3v2y5z+m1vzKKX4zHqZ039ru4iI3HugxMFphxe7DTYOCpnpyYMyp/+fPSI79pXNgvPzG2VO//2dBcZKLg+1lTkwYfNqn8naflm7eKS9zGjR5eZdMqf/QuCTL2/OV2NvsDA39l7umYm9qYrHd4LY+8z6ubF31z6JvWeD2Ns2IgIe3WHsmUeJve3BnP5HPxJt/qmpn+E5vWnK6n348J9zDru7BvGiHtMVj8aUTslWJCPyTT1bnLApKaKEC9IRJsseF591dBHGWLBXekxhzK4hFtTI3/NnCWNagTBmRJ8ljBkKKYbXC9pOBSKMoTCm48s+fTwyI4xZFVI8rO0cEcbXEIw8Gs7DhTG1QBhzjmDkUWw9pjCmo6hLHBtnVQDUltVozw+EMSMaJecwwcij4UzolANhTDULZ+E1fBLirE2IMGZUk97a9BS1bwSnP1cYsy4QxjyqrbNj7xjCmFOG/5bG3qWNKZaappTxClfv0+njPmc/fT29bcs3mm3D888DcG+riDC+0mcwWfbYPmzRk5P94L3jNkMFl40DFjnT5/muCp6veLi9DMiee9GW/deRksfuMYuD0w6HMg47Ry1GS0ILLdl+dW8/pEg+3yU01o0DQvfcN27TPiV7/NuHLSbLPqv7DAzX54mDcr3HOoSa+VKPwXTFZ8uwCD22TsjebH/eZfOQScb0eaHbwPEUj3ZI2yc7K1Qc2e+dKHnsGLHoyspe8t4xm+GiUDvzltBvfSU4faV49lCFguWzbsBkpOixZ8zm4JRDV4BzrOTxap9J2fZ5MsQZUF5f6DbImD6bBk0GCi77J2xaJx16c7JfPlXxebnXwHKFngrwREC1fbnXYLIi++a9WYe2SYd9EzYDBZfNg5KP8Hy3UaUqAzx1qELZ9lnbJ/TkXaMWhzIOndMOu0ctRooe6wZMCpaIdaoAp6cUz3VVyJs+6wdMhguyN98x7dCVddgxYjFR8ljTa1JxZnA+2iEU5hd7DDKGz5Yhk768S8uETcuEU/XJtOHzUo+BFdCNBWflyNjLSuztmx171vFjb1cQe53Tc2OvOCv2Hp4VexnTl8o6Q0My3Q0Xt0/gODkX8mIx+VbzPLhSWLo3nJ4mEYVLFyVoTEY4dz7UxaXggOvJPucFC4Tm+PalkmX27tNk7nP1MqFZXrwozryUjq5JBpQGNCeF2HHxwjipqNBWAd51mlAk3740Tm1C58KFMeanI6QC1lpM16iJSUbVZYsSJCIa1y6X671zRZK4Lllg9Umd8+YLjbMpKdTRdEzIIfVxnSuXxIlFNN65QtpeszxBIqpx6aI4jSnJ1qqNyx6/7YkwhGRqia26Jjh1TeOqpUKbvWhhnHlpnageJRFk5DUGOC9ZJFl71ywPcK4QyuuVS+LUB9lo81MRamJSJCMR0JAbknqQgQfXBTivXZ4kEZEMxMaEzrlBdp3tKTwle96SDSg4o7rGu2b5JBnTuGRRnOaUztnNkhHoA/PTisak+KQmJlRhLcAZCXDWxAXngnSEREQjFtGI6MKWa0pFuHSxZMKFON+5IklUlwzEuoRkFzanItQnpN9LRSV7sSGhc8WSBHGdqk+uWxH65Cix58v+/IULoTauHxF77whi76KFQewRIxmT2JuXEirvxUGGYRh7754Ve/VxHd72Nim6mU7/DGfkeZ4M7T1PaqkBHRkb14ehoovh+IyVPPKWT9bwmTIk93q0JLnR/XkXXym6MlK6qjfnYvuKoYJL2Zbc7ZzpkzN9JioeZUcxXJTP9OUkt7kr6+ApxUDexXIVI0WPku0zVfHJGJIHP172qLg+gwUX14eeoG131sFVMJB3MR3FWEmSiqYNjynDoxDYarqKgYKH5yu6s2JrT9bF9WCo4FJxZmzNmj6TFclPHylKrntfzkUFOJUS3LYn75dtySHPmD650FZb7oHryT2p4vSlrekqRkseRVvy3jOBrWMl4R2EOKu25uTvwYKL4aqqTzKm3KeSFeD05D56StEVtO3LuTie+LMc4gz8OVkW+4eLknvelw9szTj4SnBbnnAOSrZisiL3J2/6jJc8Ko7PUMHF8eV+hj7xQp+EOC2f6YonOC2fsZLgEFuZ65NjxV5FYm+kePTY6wtibzjEWZnx5zFjLyOx1593MTwlte9KJRn52vYJP14nZ0+vaTPVPYPso9qYUDNTUQ09oHxGdfAjoJDeNxnki6eCXrwmLt9p6ZiGjmioRXWkZ9A1tCC3PKJBMqqjB7nbADUxXcodxaS3SkY1okEuezwi2WaJiEZE00jF5Fw1Qdt0TOiV6ZjITSUiWrUUlq84wlY0uV7V1lnXS0Q04rq85vkydw3bVm2N62iBHbom544E1wvxJSIaEX3G1jk4tcBmPcxBn8nZj+qQjEIkvK/a3PuqBfZENJnbxnRwg3WEaEBBjmhyHzWOxJkKbBVqrLwW0mSTEU1wRbWZ682+R5EQp/gjpkuVm0hwD0IfzMYZ2poMrhebhXPG1vA6c3EeK/YiR4m9dGzGZh2NZFQnqh0Ze9GjxV5cr5baimjIPD4sxa2feD998j70YWnfujpAyAk64ryoPjMc0wBdE4fLQybkEE3TqE/ITayLS0DXxMXRqZgEI4GTohEtGM7KZ+V6cu7amDg1HZMASQaBHY9owVBfbJrdtj4Q6KiJiVNFwWYmDTeuy2sRXUQqdKjaGratjQc4Ay69rhRKzdgqAhdH4owED3QsCMR4oChzLFurOONalbASi8w8AHFdIx3c89q4BGsVZ3zG1ohOlffvA1EfohF5LaJJeSwtuB5IGz24N6GtiWBh1lfip5q42BAOwRuSgrc2LmSi0CepmGgBRHX5gpiNM2xbPwtnJMAUj1Cd5sWD80R08bk2p+3c2AttDWMvfpTYa0jqc2MvdljscezYC20N/UkyKVPet+ihP3mH95WK/OzuBqB12sbxoS/vUrFlaJczZRg6XpJh6GBB6KPdORlKdkzJEKsr62AHw7ZSMFydNmRYN1aWYftAQYbG4fCzfcrBVzKENR3FUEGGgBNlj6lgODkSDNn6cg6uB53BkO7gtIPrQ2/epeLK8C1v+kxWPCbKMjQcKrgYrk9vzsVV0DEtbQ9lHJxguB0O5TOmz3RFhuglS6YTlitTAj/AqYKhs+nJMLxoy+czhtg6WpIhc3/exfEUhzIzOL0Ap+EqhooeBUumBlOGDLmHizLV6AuG8yHOzozg7Ms5VBzFSNElZ8mQd6Is5xkuyjSmJ+viK7le1SfeXJ9kDI9pQ34v2r5MrQJbVYDTU3Iu0xWcMiz3mJqN0wmmOr6q2toxLTh7czJEHw5snSx7TFbEJyNFF8NR9OaFxn1wesafs2NvtOSRDWJvoiyxN1QQnMeMvYJbnYJmTPk3Fvjz8NjrCGKvO/AJY2OygGdZP8PD+1hMJIFsG66+GoBfWJkmGVVcsUQWuM6bL1RGz5dhbzqmE1tIoEcm1MT3rpSpwXUrkqRjsjg2Ly3qJ+G37cK0LAJetkgWU8LFuPeuTBHRZXGlNiG0x4akTl1Ceq6oTnVx7sqlstATLlJdf3qSeETjqiWywHXBgjh1cVFzUUAiKsPd+oTOVUuF8vme08XWd65IkorqXL5YFrjOmx8jFZVpgePL4tglepyauOjL6QFOTRPba6uLY6KAE4vISGJ+Sq53ebDAFS5SvXdliqgui2V1CVlwakjo1CdkqhALFhwbAv28RGRmkepdgZbclUsSNCZ1zp8vdjmBSmwqKqpEtQmNq5bJAlfVJ8uTpKIaly+OMy8Vqfb2PrKVVRvXuXSxLORdtyKJFuCMaBpXL09QGxecTckItUEvqusiRdYQ6BKmojrvCnC+5/QUMV0WAesTOhcuiFOX0KqFTOMR6ckbEjpXLUlUdQNBFtaSUe01Yy++UEYzh8fetcsl9i47WuzVyCLgsWLv6mUJGhI6nHsuLFwoJa5/ZhfyLAsmJ+Xn008DcGeL1BN7sdtgvOSxdUgUTFsnbaF0FlzW9gsV8elO2Ta5P1BCfaKjTMFWvNJnMlx02TFiVamj20csRoouq/tMiraqbrvd31LCDaigOcNn7YAQVnaP2lUq5+ZBoUu+2G1QcfzqdtRDbSVMV/Fctyjebho06cnJNtjecYu+nMuGAaHdPtsllM9QhfexDqnB9lKPwVjJY9uwFVBVpZ7dUMFlTZ9s2T0ZUGrvb5Gadk8erJC3hJI5VHDZOWrTNik4tw7L9tDLvQYlR/F4sB31QGupSu3NVGQbrC8n24NCQXbZNGQyWfZ4vlu2Jh9pk7aPtEttuxd6DCbKHpuHRGG2ZcJm75hsTa4fMMkasu3m+IoHAp88frBMyVa83CtbWdtGrCrNdceIxVDBFQqtJT5RSnFfSwlPKZ7qrJAL6LqDAc7WKZtDQW26sZLHyz0GZduvboU+2Co1A5/rqjBl+GwYNOnLuewbt9g/Icq9Gwdla/K5btmafKhNbH20XWoVvthtMFGNPXdO7L3abxw19n508Oix1zElW77Hi70pw4OtW2FwUHr7t2DL7uRMzrEsGd6Xy/LwL19O18AwWd+h4vikY5IkE9UllVEpWYixPOldws9UHJ8zT1tG98Aw6ZiO4YjWue3LwhSAp2SObbqK1FHahOcyXJ9EJKBiajKXcz1ZdDrW9cLXTVcRi0jaLkponLYnc8PXsjU1C6dC2sd0MN8gTg1wlczTw/O+lq3xCHg+EOB0jmPrHJ8chvP1+CQV07E8WaRUb9AnyYiMLPQQpy8+eUM4kanym8H54469c2pTLPF9aG6WbexE4meYWtvXJw//N78JwN+vmaTs+Pxgl6SnPtpRZueozfp+k+e7KrRPOUGFWY9vbM3j+YpPrpWaYV/eLPTG2/eV6Mq6PN1ZkWqlwxZPBZVP/2evpOF+OUjb/OTaLK6v+ObWAhNlj3v3l2mblJTPsBrsI+1lBvIu398labhhiul/r5c03O/uKDBccHmwtcTeMZs1vQYv9RgcmLC5v6XEWMnl29slDfe/1knbL2zMVaut9uYcHj9YZvuIpLaGlVbv2ldi2vD42pY8vhKcvlJ8dUuerOFx5/4SnRmXZw9V2DRosm3E4okOqWV3yx5Jw/1ikDL8X+skDfdb24Ra+8MDJVomHF7qMXi1z2TvmM3DbVLL7ns7JQ03TDH97AZJw/3+TklPfbi9zO5RqTr7Yo9QiO87UGa87HHjNknD/VTgky9ukjTc2/YU6c46/Ohgma3DFpsGzaByrssd+yQN9yubJQ33k2uzeErx9S15pised+8r0T7l8FxXhQ0DJjtGJWW4N+fwg6D6b5je/F/rJA33O9sLjBZd7m8psT+o5vtKn8H+cZsHW6WW3U07Cliu4r8DnJ/bkDsy9kYk9l7oFgrxvftLTL5W7O2V2HsqiL0tQxJ7XWHsmUePvdGyC48/Lmm4k5M/w2m4p6i1P5G2p2w9+dr+fFNre3sF5Kc/DTfeyJ/f18Z/vKuBm3cW+dB5aTYOWpzVHK2KRp7dLDXefvu8Gr67s8Cn3tnIP68WauSfP9DGv1zdwD0HivzSqjT7xm0WBXLKIyWXyxcneK6rwp9cUsdXN+e44/eEHvv1G5r54sYcf31FPY93lLluRZKerEM6WIQ7OO1w/elJHmor8f8CGue9fwC/f6/UwbtxW54/uqiWl3oNLl4Yr4pgLquLsHPU5tfOTvE/e0v82zUN/PuaDA/8kVAxP/nORm7dXeQ3zk2z5TBq7XnzY6zpM/nwBTMU4n96OcMDf6T4q4fa+cer6rmvtcwNK5O0Tjo0p2S7sD/v8o5lCZ7srPCXl9bxxU057vp9+PDdLXz1/c18eXOOj15Wz5OdUrNvIO8Sj4gkduukzfvPSHFfQCH+1Fqhq/7Bva189vpGbtohlNM1fQbnz49XBUNXNkbZMmTy62+r4ZbdBf7jukb+NfDJn94fUE73FvngOWl2jFgsr4/i+YqJis/FC6W+4B9cVMM3thb4nw8rPnxPK9/4QDOfXZ/j799ez0PtZd5zWlL06AOp8O6sy3UrEjwWUIg/v1Hoqh+5R+jOX9uS588uqeW5boPLF8cZKXromshc7x23+cUzAwrxO6Qe3X1/CH/0w1b+692N3LyzyG+fX8P6AZNzmqMUbUXZ9jmrOcaGAZPfOq+G7x0r9vYX+aUz0+wdt1hcGz0y9i6u46tb5sbeFzbm+Oy181n+7OPw7ncLtTaR+Bmm1hqGZCFlMrBkCb2Dw0x5DpYrUkq2F8x1lczroxrYvsxbw89YrmLliqX0DY5U/05ENRxPVbc7fR9ir6ON5SniusyNdWRe7/qyv3u8tqGtAbeDyJux9c3gnE0/foM4vcBW/U3gPGGfKMm7eDM+8V4nTttTxP63cb4OW8+sSbIERBizrk727H9mqbWhXNZttwHw6c1SI/zeAzK/fK5L6p9vHbZY22dyKOPyWFB37pY9Qm8MZZ2+v6tA3pSaaD1Zh5d7DXaN2OwetXmpx6A35/BAUHPseztlSvG1LXlcX3HbniJTFY/HO8p0ZlzWBnXQD0zYPNtVYbggElQVx+dbgdTWN7flMV2p2zZalDWE1kmHTYMmG4LadE8eFBmp2/eKXNY3AlrlTTsKlGyRVxrIuzzfbbBvTGqmrek16Mq6PNJWJmt4/GB3IZjLC7X25t1Sz/3hdpm/v9Ir0kx7x2xe6Jbdh/tapIbcTSHOrXkcT/E/e4tMlj2e6BBZsHX9JpuHLFomHJ4+JDJSd+2XOX0otfWt7SKXdfd+mQs/e6jCgQmHzUMW6/tNDk47PNEhMlK37S3i+IqvBTi/u7NA0fJ5oLVEX87hxR6DPaM2O0csVvcI5fShtjI50+f7u0Qu66tbhFp7y+4CGUOkvbqCuoDbApzPdQnd+YdBTcDv7BCc39iax/YUt+8rMl4Saa+2Kal9t2nQpG3S4anOCmMllzv3CbX2mwHOb+/IV2NvKIi9/bNirzOMvcpM7H11Sw6A7wWx92CbUIhf6jl67OWPEnu37ikyXnaFdHbokHSA0ydeGvLk7OlDAQ3Lgq4uuOACtnQMEE1KfvSCdIS8JQKOnpJv91RMI2/6zE/rjJY8ltZFGS64XPm2FezsHGRpbYSJik9zSsQf48ESqh3sCWcMn0U1EVHSOWcFOw8Osqw+ymhRykBNGz71CR3TkW/qqA4VR9GY0JmseCyunXW9sG3JZWFNhJzhUxMXaWiF9AhFW2wZL3ksOczWZXVRxkse89IixjizTy8ZbjnTZ8FRcO7qHGRJbYTJik9TUuiqsSCb2XIlH2G64rOo9jg44zqmJ2IP0QhUbCHATFQ8lhwFZ+iTnCVCla4vvXUyoMfOOw7O5rROyRKhSqWk8mxtTCc7C+cVs2wdKbosqY0wVZEKsYajiOgygjJcEcR8LZwLayNkDZ+6uOwaaEiPW7Z9GlM6E+XDcAa2zsF5lNibl9YZewtjb6TocuW8NMtKJViyRIQ0kknZrz/O8dPX0zsOZLOSnLN+PQBPdUuF1C3DFlOGz75xm4GCR3fWoX3aZrQkstIFW7F+wMRTiucDSepX+0zKjhLaZdmjbdKhL+fSl3NpmXCqdMmyLRVmAZ7vNvB8FdA7FbsCamrHtE13xmEwL3LG04bPliGrSjEFkXe2PSW0UsOvUn87M7JnPlJy2TNmkzd9Ng5aOP6MVPMrvSaG4wd0VpGx7s+7dGdd2qdErnvnqEXRFjlnP8CplArowYJzvOzRNiX7z/15lwOTDpMVj63DQjl9pVdwvtAjlNcNgyZ50xdaa8mlM6CqDhU89o7bZEyfzUMWljeDM6Tabh6yyJh+QDP16Mo4HJxyGC267B4Vaej1gyauP+OTNX0mZcdn24jFVNmjJfBJb86lbdJhoiy04pKjeLXfRAU4PRX4xFZVunDblOQT9OddDkzYVTqz4fi8Etj6Yo9QmDcOiiT3njGb4aLg7Mw4DBdd9ozb5AyfTYMWtjfjk9W9Bqar2DJsMW347J8Vex1B7O0aE1ny9QMigX147G0flthrnRV7rZOvHXvrB0R+nQMHJCuvXH5LJLBPzoW8SES+zTwPzjsPgCsXSZbbOc0x6uIapzdEaUjoOL7s0zYkdFY1SbGL8+bHiGiSgQdwwQKh0p7ZJG2W10dJR2dywBsSOmc1R0lEpRgCSIGDiK5x3vw46ZjGqsZYUMk1WiXPRPQodXEpLhGLSFENkAIHUZ2AFivFEZoDDTelhFCxshHScSnKENVmijJctFAKSpzVLEU9TmuIUhfX8RRYrhTmOLNJsvQuWBBDD3Bqmsb584W2eWZTlIakznIlmEICT31CKKyJiMZFCwXnJQvjRDQ4d16cdFzuYXMyUiX5SPsotXG59zF9BudFC+PEInBOs9B/T2+I0pTUq1TgurjOGY2SX3/ePLlO6JMLF8RIRjTOapJCICvqI9TEhXpcl9CpT+qsaoqSjGpcMD+GFuCMBDjTUY1VTeITTYsS1yVLUqrPSiGMeETjwgVyvUsWiU/OnR+jJhb4JBUhEeTep2IaSkWpCX2iz/LJghmc1dhL6jjeTOyd0SgFSM6bL3FzeOyd1Syxt+Kw2Ks/TuzVxHRZuGtsfN1SWcc7Ts6ePixrpVR1DjNallJRUnoIKZvkKsqOiBOGpZEcX8o6+UpojEBQNkgq1FqelKYqO9K+YPnVkkxSTkqyNSYqUkJpOiiVFZYgKtlSDikscWV7YpMflKKCmVJVmaDUUS4ou1UOyjaZQckpx1NkzLB8lrSdrPh4aratCsNV1XJRpiclqsJSSUrNlEMKy0DlLFk9L9pSZsoIyjeFJbZcJdep4gSmDSmJFeIsBuWwDFcFtkopqLA0lNgqZa4y5oxPDFdRtmd8krf8oNRWgHO2TxTVklkFS0pLheWiwvJRYekrkBJRSs2UgQpLdRWP5c9ZtoY+mTakJJbYOlNiynTEVseTUly+mu0T74jYM5y5sZcPbJ02JG5Cn7yZ2AvLlYWlsqp59573lpS1Ojkf+vBQSoAiq6ySlaZQqGo2lB/8m3lvJssq/Bm28YI2atbnfSXSTiEDzgvWOOacQ4GPQil12PXmtnGr15v56cNhtgbXC9sG53er11PVrDRUaOMMTma3nXUdpUTQgRDLse5NeA5/Ls7Zn/ORz6pZdiuObOPNshl1OE4CP6k5tlbbqFltQvuCezP7vjH7urPxHvbziHsUtAnP4R7mz/AeqcA+f9b5qrYe9jO8N4dfV/w5N/b8WW1mx96c+1z18dw4msEtr0v1EPWWVKyFk3V4r+sQjwvYJUsAOL0+Vi09nIxKmeLauEbC13CDqibz0zIsXVwrJZyX14flmKNBGWEhoTQFtdpAaKfJmBaUP4alQXni5fUzZaBjEY35qUhQU04onHEd3JROIhqUMtapXm9ZXVDSuUbKTc9P69TEdSK6j1Ia6bjO/LRowomtM22X1sn0YWFaD3BGqI1r+L5GIqJIxgRHLDJTonp5vfxcWhclGpRaTsVEpjsZ8MVB7tvCtNBDl9bNwolIQIeS1+mYHpSMluHyvLSUfw5LNi+ri1TbRjRpmwh8UhMXWq+nhIgSlrGWstYzPllaG+CsEZ80B2o9PhCLiD8XpIWIE9q6IsC5OPTJLJzxQLOgijPwydJZtuqBrfEAU6iZIBRrnXkpNQfn8roZf+qHx15AI3YDnbsFrzP2mufE3ow/o8eIvUREkxTcVEqIaNETf2RPzp7edWXBwnFg3z4ANg3L4ljbpEPBVHRnXSbKHiNFl4GCS8b06ZwWiuf+CRvPV2wfkcy+veOy0NYxZZM1ffpyLqMlj7GSR2/OIWf6dEzZmK5iz7i02T5i4flyrrLj05lxmDY8BvIuwwWXiYpPT9alYClaJx1sD3aOCu1x56iN7UPLpE3B9unKuExWPIYKHgMFj6mKx6GMQ9n2OTBh4yrYMSJtd49ZWK6ibcohZ/n0ZGVRa6QkC1VZw6djysFwFPvGbXwlOJVS7B23MR3FwWmHrOnTn3cZKQmFszfnkDd92qeEfrtnTHDuGLFwFYLTlns4XfEYLLgMFz0my2J/0fJpnXRwDsPpeNAy6VC0/MAnPkOBT6YNj85pwbl/QuTLdwQ+2T0mPmmfssmZPr05h7Gyx2jRoy8n/uyYFpx7xmyUUmwbtvCU4K4EODNGgLPoMl726Mk65C2ftimhtO4KbN0xIspLByZsSrZPV8ZhyvAYLIhfJiseXVmhJLdMCo07xLlr1D4i9sZnxd604XFw2qF8nNgTnDOx15d3yRnHjr19ga309Mh2nWHIvxM8Tv4tu54eOO88tncOoMWFvzwvpVOwfVJRHS9QJJ1RT9WZKMt2zWjJ5fKzV7Dn0CCLa6NMVkRhtmILAUZDiC81cS3YHoowVnK57OwV7D40yJJa2VJaWCPbKnWB8mpEEzVcw5FtvGnDZ2HNzPWqbcse89NSo6wmJppqikAl1pZttcnDbA3bTpYDJV1bkYjKkM/1IR0V9dR5KZ3xsmwVzsa5qEa23RqSorwa1eWb3Qoq+2YNnwVHs7XksaBGtsnqAtVfLRAnqTg+9UmdqYpsLR3edqIcbC+aQnLxfBm6JqKyNXk0nFWflEVJt2QrEhEZzs7dmjzSJ2MldwZnoPob0WVkYrqK+mAb7Kg4yx4L0jo5U7ZR7XDLTtcoOz6NSZ3J18L5E469y5tTLK1URA03XMz7mdyysyzZorAsePBBAL61S0gPPzpYZqTksbZPdNX3jNtsGRLq6vPdonT6QFsJz1fcsrsIwA9byuRNoXcO5IVCeWDC5sCEw/oBoWc+3Vkhb/nce0DojbfuLuL6igfbSkwZQh/tzgpFdfeYTfuUzZp+k9GSJO5UHNFwB7h9r1BrH2svM1HyeKVXElV2jlpsHxZK8Ms9oiD7SHtZaqztEVvvCWqwPdlZYajosa7fEHXZcamd1peX5JCs6XN/q6jg3rK7GFBsy+Qsoev251w2BbXoWoKabUMFlyc7KxQtn3v3i6237S7ieIqH2ktMVYQ+2pVx2DZisWtU6K6vBIq1j3cIlfaOvdL2zr0lDMfn8Y4yY0WPNX0mB6dtdgW197qzQlCarkhilOMrbg18EtbUe+qQJNOsHzBpCXBuHDAZyEuyj9SBE2rtLbuLeErxQGuZjOnzXJfUIdw8JMSgtkmHtf0mw0WPJw5WKNmSOARw2x5JgnqkrcxkWajLh6aFxrtjROjLq3sNxssej7WXsVzF7Xuk7V37SkfEXvvU64y9A3Njb0MQe/uD2BvIHxl7twSx90BbSRY+164VAlouJ/9O8Dg5e/rZabjZLCxeTN/QCJOuDLPiEUkxjQRUTKFxSopjLKJVP2N7itOXL6V/aKT6dzwilUOq6anBHP14bcJze76CgMbpKekhjts20LYLF2jClM/XY+tsnCqw9Xg4w/ddX3pr7Q3irKYMa9IruG8UZ+CTN4LzaD6ZjfO1fDIb5+v2yWGp0br2xnD+pGJvVTrJEk2bScM9GSrcaJr20eDfV2a99iFN027QNO3f3tRJw1p2lgVf/CIAf/niOGXH51vb8vTlHB5oKbFt2GJNr8lTnRVaJ+1qyuznN+bwfMW/rM4A8N/rs9V0zoPTUjFW0i8tHm0vcyjj8L2dBfKWz6fXZQH4l9UZXF/xxU05Jsoe/7O3yIEJm6cPVXil12THiMV9B0r0512+uS1PxfH5xKvS9t/XZDBdSQMeKrjcu7/EriDt8rkug73jNnfuE2rtl4Nqqv/2itj6ybVZirbPd7YX6Mk6PNRarqZ7PnmwQvuUzS27i0wbXrWyzb+szlQr3WQNj5t3F+iYkiqs6/tNtgxZPNQmqbnf2SHpryHF9V9XZ3A8qSY7XvK4Y1+R/RM2z3YZvNxjsHPU5t79kvr89a15DNfn39eIrf+xJoPhSGXYwYLLfQdK7BiRKkDPBCm5t+8tMl72+OKmHM4sn/zXuiwFy+e7Owp0ZaTi8KZBi/UDJo93lDk47fD9XZJW/N/rs6gAp6cUn9uQC1Jei7RO2jzZWWFtn8m2YYsHW4Va++3tks4cUlz/7ZUMtqf4yuYco0WXu/aX2Dsu6ckv9khl4HuCdOKvbsljuYqPBz75xKvZauz1510eaCkFadEmTx2q0DJhc9veIpOvFXs7C3ROOzzaLrG38fDYM4+MvS9szAm19sEHobUVxsdhYuJNPVKzjxPq6TVNuwHoUUr1aJr2CHALkAFWKaUe1TTto8BOpdTusM0pau3J0/aUrSdf258Gau2q4N+tQE/w+weAl4P3e4AbgN1HbX2sIxTRqKuDz34Wvv51/vrBdv7l2npu213kN86tYdOgyVlNMUqOJFic1RRl46DFb54rlWD//doGPr5GqJF/9VAb/3BVA/e3lPjAqhT7J2wWpmULZ7TkcemiOC/0GPzhRVIJ9tYPCz32y+9r4qub8/zFZXU81Vnh6mUJenMu6Zhkt3VmHN61IsmjHeUqjfPO3xN67H+/u4nv7ijwkQtqeKXP4MIFcaYMH89XLK2LsnvM4pfPTHHX/hL/HNA47/0D+IsH2vj4tQ1Vyum2YYuVjVGsILHm3HlSIfVD50kl2P98ZyP/9kqWe/9A8bePtPN3V9bzUFuZ965M0TZl0xxsZw0WpDrvM10V/vTiOr62Nc9tHxZ67Bff28Q3tub500vqeLarwpVLEgwWpGptc0qnbcrhPacneaitzN9eWcdn1wst90/vb+VT72zk5l1COV3Xb3LuvFg1Oei0hijbRyx+7ew0d+wt8i/XNPCJNVl++Ifwlw+GlNMSv3xWit2jNsvqI3i+JMNcsCDOK30GH7lAKsHe/DuKP/hhG195fxNf2pjnb66o47EOqSTcOYta25uboRD/xaV1fHlznts/IlVyZ9OdX+wxuGxxnNGSVK1dWBNh/4TNB85IcV9Lmb9/ez2fXp/l7t+HP7u/lU+8s/GosVe2Fauaomwesvg/b0tz6zFi774WqSS8P6B1A4yVPC5ZFFCIL6zlxu15bvndmdj7yuY8/3X1PJa/8CS8850z1NoVK07ooX3L5vSapr0MfBz4K+AWpdTuYCTwAaXUx8PPve6evlwWyazxcTjtNDr6higiiqK1cZFKiulaNeEhFhGyRU1Mr36mZPucffoyDvUPUxvXKdtCCLE8kXICSYBIRIQ8U3OUNuG5Ko4QQlwvkGbSRKgyFT329aq2OkKyCJNqoroQYNKvw1bTU28cpyMkHTvAqSG2JiNaFWfR9jnntXD60i6iCTEkNet6x2p7Ijgtj6osmOeLUGWIM7xeZ/8wdbOuF+J0DvPJ0XAe3vb14DymP48Se+ZhOA+/7uuJvaPZem5diiWeB/PmnVxyWZqmXQ68PHsYf0KHacLoqKTi3ncfAN/YmaPi+NUKqq/0Ch1y15jFpiGTnqzLc4cMMoZIPnm+VCgFuGt/qSokGYo17h+32T9us67fYKDg8aNgVfuuYAX++zsLuL6qVsJ9tsugJysrxTtHRdxwdY/JSNHl0fYyRlDVFGT11XIVD7eVGSu5vNRj0BGIcG4dMjk07fBCt9RFe6BVaqz9YJe0vWNvkbLt81iHrN6/2idVbveM2WwYlJp4T3dWyJoe9xwQQczv7xSK7T37S+QCccZQfDMUuFzbZzJU9Hj8oNRWu3OvXO/mXbJ6f3+LUGCf7zboyrhsHTKrIo4v9RiMllwebpPV+9uClelb9wjVNqz2urpXaMM7Ry22DJl0Z1ye7zKYqnjc3yKr99/fJT65c59QfJ84WGGw4LG2X2TE9o7ZbBgw6c+7IvRp+tyzv4RSipt3FvCU4t4DJbKGxzOHKvQGgpa7xyxaJ23W9Mrq/WMdZcq2zx0Bzlt2FQMBUqE0v9gtFYC3B9WLD04LvXe85PFQm6zehyvw/xNUJX60vcxwcW7shWKgzx4ymJ4VezcHsXf3vrmxt67fOGrsFSyfu4PYuzmIvR8eKDFRceGVV2SNK5uVfyd4vFUZeTcopb4a/J4DmoPfG4E5BOD+/n4++lH5AvrgBz/IBz/4wSPPFo/D/PmSnPNLvwTA759XRzqmeN/KFAtrIrx9aYKaQIbYVdIjpGNSZOCXz0oT0TU+dJ7sZ/7aWSnq4hrXn5Zkfo0QO5IBvfG0BiF8vOe0JLVxjV89W75FP3ReDVFd45fOTNOY0nnn8gSNKakHFw0ksBfWRGhO6bz/jBSpmM7/eZtUE/3Nc9Mkoho3nJFifjrCO5ZJ/bSlQRcY1oZrTun8wqoUsYjGb50nbT94Tpp0TOO9K5MsromQWCL16TwFbkDFTJ4mNdd+5cwUuiY4dU3jV85KUZ8QKe75QZ22eEQKNyyvE5LIe08XmewPniPX+61z08QiGr94ZormpM61y0W2e0Faqq7EIrAgHaE5rXPDGSlSUZ3fOFfa/sbb0qSi8vr8mghXLRW5cMcLJLBjGnXxBE1JnV88M01M1/jQuYFPzk5RG9N4z+nJICtPatspJT1uXVzn+tOEPPOrZ4nE94fOqyGiafzymSnqkyJv3ZyK0JjQiUakMMaSWiH9vHdlinRM4/87Z8Yn8YjGB1almJfSuWa5SGEvrpHdmEQwlZmX1vnAGSkSUY3fDHD++tvSpGPi5zD2agMKsaskI682JjLgh8fer579+mKv7iix98tnpZmXjMDb3w7Lls2IaJzg8Zas3ocPfDCcfwiZ2xP8XD3786effjq33nort95669EfeJCMvEJBHvrdMnhYOyj0xv3jNjnL51DGYawkmWO9WZepikfblEPFFhqspxSbhsKsMxvDVbRM2mQMydoaKkq2WlfGIWt4HJiUz4QZY5uGJCtq16hFyZYMuamKZPMNFFzGypJtlg8opZar2DosbTcPCTVz77hNwfI5OC1ZdQN5l768ZPN1TDkUbcmMc33FpkFpu23YwvQUByYke/BQxmG05DFUcOnJuUwZQg0uO5Jt5gc4lVLsHJVMtdZJyR7syboMFVxGix6HspKld2BCsr/CjLHNQ3L93WOCs33KYSLEmXcZL3kczDgULMFpe4otwX3dElBt947ZFEzJWqz6JOcyWfZpn3Yo2Yrdo3I/Z3wimWoHJmyyhk9X1mGk6DFcFBpxxvBombQxHMWOUcnI2zho4SvBXbEDnBWPnlyAsySZjjlT6K+WJ/czxOn4ir1jFgVbMhMnKz59+QBnWbLqipbPnjELxxPKMMDWYcmS3D8uWXWhT2ZiTzIAy7Nib2Pgz52HxV53Vmi8gnMm9iqHx56ScxVtXwQ0pqdlratSeXMP6qzjhHr64CH/iqZpH0d6998O5vJXBu/l3tSQPxKRbzSlqosWZzcJrXNpXYR0VGNhWnqyVFRh+1J7fUmQP76iPooOrGoUeKc1CPVySW2UmiAfPKyLFtEi1MR0lgY50qc3CL1xVWMUXYMV9VGSQY58bUzDS+nVGm1ujWRjLauT3OmVDdFq24guudvJqORy18Wlna8kM07y1eX8ugarmqTtykaxY2mt2LiwRnB6viIVFXGJME/+tIYouqaxqjGKpmmcVh8lHuTkC04V1G6bqV+3tC5CNCL0UIAzGqNENFhRJ/TOxTUR6uIaEKlSchf58nNZneSzn9E40zYacA6Ss2xNRMJqroI9EdVmcAZtT28QnsDSumg1d70uruMrRTyiSMd1ltZFiUUEl6YJZVjXBHc8GuCcxWOIBvPsVGyWT4LrrWoSnMvrha67uFY4DRoRuTdBvn4yqrG8PjoH58qGaMBXOHrsVf05K/bObDp67C0IYg8kfyEdxF788NgjiL2oNlPoIhaTUfAJHif00CulVgNNR3n9OCt1xz2xkG00rbp9Z7gKH4IyyMFPX+Eq0Sv3fVk08lGYrixOzvz0Z7VVOJ7CjWjVBS5PiW65Cj47u63lCVMsvK4TZJ6Idr2km860VVVbUWFbSbf0fKrKOZ6vVduarrxmODM2KyVpsyFO11e4vlzbDWxRiiNwWsHrVZy+1JRTmmCWe4TYNqutOhxnYGtEp1oiO8TJYddVc3CKT5zAXleFbdUR9yhsG547LPvsQ2Crwpp1/vC+KqXmXNdTCjtcyEPN8idz7pHhzMbJDE5f0nDdSDgt4aj3N4yf2TjdIDXaD+8Rao6ts2NvxlY1RznHC+6Nf4zY8xSytuV5M8/FCR4nJ8tOKRniRyKQF50y4SlHKFji2LKjqIlLYFiewvY0So44smD5KISrDVCwJIiKtvDCy44ioktmVMWRB6Jk+3hKkbfkhmdNcVbBEt53yRaHVRwpkgBQcYS/X7QkGHKWXC83u60PZcfH8iRH3FeQiAiHu2qrkjYAedPHV1CyhYdecaSHd/zgep7k7Xu+8L+Vkq08pQL+uRIsjief15CijGVH7lvRnuHrhziVmrG15AhOI+AY6Jpcz/WF/+2rmfuaC2wtWArXEy58vSf8BMeDdEz85PmIrcxt6ymxx/aFgx+PyP2pOArbh5IT+MSchTO4r54vOG1PYTg+oONHoGyLLUVbbMvNut4cnLbEjeEEHIOI2O8GPvGZ1daawRnGXm1cvnwsD2pjM/7MB74/PPZmfKKI6vJFI7Envvb9I2Mv5OhTqcw8+D+zD30kAum0gDzrLAAuXpAgpsueaG1MZ1mdDAfDXrA2oXFafSRQKRFFmfPny3Dp7GYZDq5sFKWbpbXyubBqbW1ChruizCO35PxAfefMJlE+OS1Q6oloUh45Fgkrq+qc0RglpsO58+R65wZqOKuapObZ8voojQk9UGeR4edyFSUVlfNHdVH7AaoqPCsbRcVlaZ0M1WWEolXVdJJRUYcJFXM0TRR8ksGwvy6hsRgZcoblq0MVn3hErlPFqYsdqZgMTxuSsjCmBwtcuhYlHRNVnahO1dZz58uUa1VjlHRcZ1md3KOaYOGxJjhfMqZxVlOsqnoD8LZ5omyzskFUeZbWRar3pzauUR8o1CQiGmc3R6s4dU38m4jK+/UJvapxF9WkrHdt6JOIXAfE5miAMx1MN0LqMcj0hXqZaqxqihHTtTn+jOsyRagJYy+h43pB7MW1qk/Oap6LM4y90xsOiz1kulUXxl50JvZC5aezmkXlh6VLZ7br3oLh/clJuHEcIRbYNmzeDMDzvbKNsn3EImN4tE7aDBVlwagzIwtl+8ZtirbP5iHRKVvdJzTEjYMWFVuxe9RmsiKUzf68y0Deoz1YoNs1JotgG4IFmNV9oh23ZcikaPnsHbNk8S7j0JsTem3rpE3W8Ng+Iotva/tF4+zVfhM7WETKBYtnIyVZQOzKymLXgQlZ5Ns6LItGawJ9tPUDJoYr+m/TwaLdYEE01cIFwb1jNiVbsWlQNPJW9xn4SrFx0KQUUFEnK7KA2J93GSy4tE/JoteuUQvDUWwYkOu90mfi+IotwyYFSxbAxoIFzp6sLDi1TMgC1vYRC8ujquX2ar+J5QkVNGf4tE6K7lxP1qUr4zAe+KRgiU9cX2q6CU6xY9eoaNq1T4nuYH/epSNYTNw9ZlN2ZFFMKcUrvaKRt2lQtAD3jNtMBAtwfTnB2TYli5jhQuG6wCdr+szqImTeEp+MFj26sg7dOYeRklddqNs2LAuUrwZt1/Wb1cXPjBnEXmEm9sbLHnvHrDmxF2rzVWNvzGbKkIXN/rwsBndMS+ztHpOFyTD2XukTjbwtQ4FGXlubpN+Wy/LvBI+Tk3BjmgLOMKRw31lnsa97EDvikTU8GpI6ZVu0wj0VDpk1yraiIakzbXjMS0WYNjwuXLWclp4h5qUi5EyfuriG4UrCCwQJNjGhRjYlj2wTnitv+tTERWtd10R8w3JlATFv+jSlIkxXPC48czkt3UPMS0fIGB5NSaHHpqJCtlBIr1RxFPUBrbL5KLZmTY/6hB5MJ7RA3UcW5oqBOu3xcJquIqLLIp7tydZSFecxbC3Y8jnHkyFoVJf7VRsXqmvzbJyhrcfwSXwWzozpH9XW14vzwlUzth7hk8Nw1sSO75Nj4ax7LZ+8kdg7/B6ZHvVx/fXF3iyclzSmWWKaspjX0CC9fTp93Ofsp49aa5owPCyLeHfcAcDntoju/f2tZYYKHi90S5LD9mGLdf0mhzIOTxwsM1XxuGOvJEh8M9BYv3V3kZwpSSS9OZdXeg12jVnsHrNY3WvQlxMt+bzlc0uQJPPNraI9fufeEpNljx91lumcdljfL8SOAxM2z3dXGC563Nci1NrvBgkZ395RwHQliWSkJEkkrZM2m4csNg5adEw5PN1ZYaLsc9d+qab6rW3S9uadUoPtwdYyg3lJ7Nk/brNjxOLVfpOurMvjHWUyhsf/7BFK7Te3Sk272/YUyRqSmNKTk+q2O0dFD/7lHoOBvMtDrWWKls/NQeLJjdsLOJ7irn0lJio+Tx6scDDQg98ybNEyKVryo0WPH7aIInGomX/TjgKG4/PDljIjRY9nuwTn1iGpvdc5Lfr+kxVJenJ8xY0Bzh/sKlKwfB5uk3qAq3sM9o4JnfeVPqGrPtpeJmt63La7iFKKb2zL4ynF7XuKTFcEZ1dG6LQ7Riz2j9u82G0wWPB4oE2q/34vSAb6VlAz8O79JcbLHk93VuiYctg0aLF5yKJtyuGZQxXGSh73HihhuYpvb5e239tROCL2DkxI7K0/Rux9I9DMvyWMvbZKNfZ2Hy32zFmxt20m9sbKLrz0EnR3i5BGJnPCj9fJ2dNb1oyQRqEghJvhEUYdG08pIpqGrxS6plU1znRNq743++fypUsZGhmZ83rYFqj+frw24c/wfmmzzvN6r3eibd8MTu0NXu+txvlGfXIsnK9l65vB+Vb55M3ifL2xd3oyyZJoVOb0Jwu19sdyGIZ8s1kWfOYzAPzR80Kt/dpmodbes7/EliGT1b0mTxwUeuPNO4Va++l1Qm/82IuSDPifrwq98dvbhVr7cFuZtf0G6/oNHmwVeuO3tgm19hNrJM3xYy8KvfG/1wm19ge7hFr7o4MVXuox2Dpscs9+odZ+ZbNQa/81oFP+88tCrf3ixhzDBZc79pbYMWLxXJfB04cM9oxZ3Lq7yFjJ5XMbhFr7jy9J24+/kqVk+3xjS56erMN9LWU2DZqs6TN5rKNC26TN93YUmDY8PhVUq/3Yi9P4SirCZg2Pm3YUaJ+yebS9zKv9UlXn/hah1n5zq1Br//0VwfkPLwq19rPrhVp76+4ie8csnuqs8EK3wfZhizv3CbX2S5uEWvvPL4ut//KyUGu/skmotXftE7rziz0GT3ZKBaJbdgu19jPrhVr7sRdDWq5Qa2/cKtTaB1qFcrq23+SR9jIdUzY3bRdq7X++KtTaj704jacU/7U2y3TF43s7C7RO2jzeUeGVPqlU88MDUknm61vylGyfjwc4//ElodZ+foNQa/9nT5HdoxbPHBK6865Ri9v3CrX2CxtzWK7inwKf/OvqTDX2+vNuNfZeDmLvwITNzbuEWnvM2Nsm1NqH2sqsC2LvoTYZPX57m1BrZ2Jvuhp7o2UX7r13hlo7Pn7Cj9fJ29MrJT29UrBwIYODg2jBt+vsn8ARr83+uWLFijfc9rXanEjbH4etPy84f5y2hsfJinN5PC45K3V18vNntmptfz/U1sKXvgRf+hL/8OhB/u4dddy5txRQTk1WNcYoB9TaVU1Rtg5bfDCgcf7z1Q18al2WO39P4+8f7eD/XlnPw20l3rcyReukzYIaqVo7Vva4eGGc1b0GH76glu/uKPDd39b4swfa+Oz1Tdy4rcCfXFzLs10VrlqaoD/vVgtHHMo4XLciyY8OVvjzS2v56pY8t/yuxkcfaucT1zXyg90Ffvs8oZyePz9W1aVfWhdl77jNLwSVYP/f2+v57IYct39E4/8+0s4/vUMop79yVoqdozan1UexPNmHP2dejI2DJr/xtjS37inyb9c08Mm1WW7/CPzDYx389eV1PNZR4d2nJemYdmhK6sQjMFT0uHxxnBe6hcb5re15vv87Gn/+QBv//e4mvr2jwB9eVMuL3RUuX5xgqOgS0yUfvWNaKMSPdZT56OV1fGlTnts+rPFXD7Xz79c2cNveIr/5tho2Dpqc0xwjb4kW/GkNUXaOWvzymWnu2V/iY++o59OBT/7fIx38/VX13B9QTveO2yytiwT67x7nL4iztt/kQ+eluXlXke/8Fvzp/W18/r1NfH1Lnr+4tI4nOytcuzxBV9YNMuQ0+vIuVy1N8MyhCn98sVClb/5djb94sJ3/elcj390Z0J17TS5eGGe87KFpsCCt0zLp8N7TkzzcVuZvrqjn8xtz/M9HNP764Xb+9ZoG7txb4v87J83WWbFXdhRnNB479v7u0Q7+dlbstUzaLDxa7J1fy3d3zo29b27L84m3z2P5y8/AtdfCypUytF++/IQer5Ozp5+9ej88DKtWcaBnCFN3yZk+9QlZFU5EJK3VU/J72ZE6ZlnDoylYbT1/1XLaeoZoClZ7axOyqh0NVlBdT2SIS5asvh7eJmt6NCUjFII6bbYn87CIBqanqI1p5C1ZZT5a28aETsmR1ehQlz4W0TAcqS0Xnv/wtrNxhqvarhLaaMlRNLwWTsunNli9j2qyqu14slJcPA7OouWTCla10SCqaVWcuWCV+Wi2NiTErmRIrVVqZpfiNXDmTZ+6hNyPWERDAW6wel+yZ3DOsTXAnbd8amOyoxKmGs/sUhzHJ7b43Q30sqK6hukEuxSvgXN27HlK5uVvKPYcRTTyOmPP8LioMc0S2xYC2s/06r1ty76kbcMTTwBwyz6ZNz/XVWG85LFp0KQz47B/wmbnqNR7e6XPIGuKKKLnK+4+IFTFR9qFNvtSr8FwwWPbsEXbpE3HlAg4jhQ9XuoxKNqywg8i3Oj6iic6KmQMjzV9UvV116jQIjszDhsHTMbKsmptOD4PtErb+1okp+CZQyJ+ub7fpDvjsHfMZveYTU/WZW2/1Kp7qrOC4ynubRFbH2orU3Z8XuiuMFry2DwktM+WSVnBHyi4rO41yJtCv/WV4PSV4rEOEVhc3WMwVJAaaa2TNh1TUkl2pOjxfLcIRj7UJrbee0BW1Z88WGG6Ijh7cy67xgRnV1ZW8ifKPs8eEtLTfQHO+1vLmK7imUOyE7FxwKQrK+KWu8Zs+nIur/YJ5fTJgxUcX3FP4JOH22V1/YUe2QHZMiw03rZJWRUfKni83GOQt3we7aigApyeUjx+UKjFr/QaDBRcdozIbsrBaakMPFoSnGXH58EQZ4vskjzVWWHK8Fnbb9KblZqCewOfrB8wmar4PN1pYHmK+1qk7QNtQp0+PPYOBLHXF8ae8Rqx1yOxtzWIvfbJw2LPmom9uwN67hMHK0wZHmzaJFvX+Xw1Q/VEjpNzeB+LiRCg68K73gXAB8+sIRVVXL0sQXM6woUL49TG9SDXG+riGhE9QX1c512nJYnoGr+0SqiK7zk9STqu8fYlcRbU6MQjsaCGmcbCGvlWv3Kp1Kx7z+nS5hdXpYjqQlOtT+hcvjjBvLROXVzSWmO6FFloTkW4elmCZFTj/WdI2xvOSJKIaly7XGillyyK05AUYogKMvJSAQ34uuVJYhGNXwjavndlilRU4x3LEsxPRbhwgdS+833JMa9PaFy5JEFtXOP605PomuDUNY13B/TgK5cmpFhGJE48IivhC9Ji6zuWJQLqrlzvF1aliOka71yRpD6pc/mSBM1JqZmna7LXXh/XaQroqIkI3LAyGeBMkYjANcsTNKV0Ll4Ypz6hY6dVNSMvEU3QkNC5bkWSmK7xi1WfCPX1qqUJKfagSc07H0mtbkjoXLkkLjhPS6Jp0jYS4KyP61yxJMGCtE46phPTRaByXkpnXirCO5YmSEU13hfiPCNFPKJx3fIkjUmdSxfHaUoKLg2R664JCmdctyJBIqJxwxmC8/0rUySj2pzYq4uLpLnnExT4EPp0GHu/eHjsLZXYi0Ukw1NDY1GtSG5fuTROOq5x/azYiwSx15jQ4cILRQK7pubkoNb+WA7XleG968LBgwDsnrCwfejKinrOUEHol+Nlj9GiS9706cs5GK4UQfCVFB4AaJ8S6mtPTopTDBc9pio+kxWP4YJHwZLCFXZQfAHgwISDpxSdQcGFvrxMLUZLUmRj2hBqZTkonGD70DopbaUohOJQxqHk+FKMw/AZL0vhibAQRcVRdGYcXF9xYNIBoG3KxvaQAhO2z1BQHGOi4jNScslZUhhCCig4qACnUoqOaXk9LPgwXBQa75ThMVT0KNhSkML25DpVnL7cM8NR9OVcsqYvBRnKHhlT7A9xur7gA6pFIbqCwh1h0ZHxssdoySMXFBYxHLmPnq84MOHM+MRT9GSlkMZQ0WPKkOIaw0WPgqXozbnVghhKCQ3XV4LbcBV9QQGPkWLgk4oUrygFOB0P2gKfHJiU+3woI/TrgbzgHAsKT2SDohnlwFbHV7QEOFsn7SNib9rwqsVW8kGxjjD2vMDWo8ZeYW7sFS1Vjb2Oqk9ka1oKaPgwNCQ9fLiVfYLHydnT67r09iA9PrAo0LRrTOjV/OpkVPLKo7oiHhVhiaiu0ZSUb+8FaWHGNKciRHR5PxGRtqmgWqkXF5psY1Inokt5JYD5aR0daErpRCNQH9dIRjRqYjqxiEYiIlVZYxGNxqSUQZqXku/QeWnpJRuTYmtdYKuvZA0iGfSeMR2akvLZ+WHblNBXw1JNdQmNdFTDVaBrYn+Iszmlo2lCS9U0rSrwMQdnTNYfauNShkn4A3KdEKemIW11hBob1aiJS7tkRJuFU2ydlxZb56fkXI1JKTNVnwhy2QNORCKqUZ8QwZGmlFxnfnoGZ2hrPKJRG9eCewQKnXhUbInqGvMCfPPTsgDWHNCbQ1tr44I3psuIr2qrLp8NbdUCn0QjVG2ticlaQLg4G4uIrfocWwOcR4m9mC44xSeBP4H5x4i9usTc2IsfNfak1FhTUpfsvXB/PhJ5S8panZwPPcjWhFJVkDFdC9Il5a2orgULaiEbTIZ3WvBZoLpYF4vIkCYapGpGgn+EbbTgvMFnpU1wDk2GYtGgdHNYSSVczNOBWLWtVrUVLbA5OHeYuqtXbZ3BwZy2zMEpbTR0VPW60eD80cNxHn5vqrYG5wnOK7YdhvMIW+XeHGGrduT9nbF15nrhPzmvVvXfzPUIMMx8LqLNYNeDex7+XY0Bbfbrc/0pmOf6M6SxxiIzbXSYEzMQ2hBcX5vlxzltZ+5DJIg9P6ggFNE1dLSZNkfEnrQN7y3M3N/oLJ/PaRtgQdfl32FbjG/2ODmH974vwxjPg5ERAHrzDp4v2xymq5iqyDAub/lkTZ+KrZgoe9ieYrjk4gMDBSnrO1yQ8sTjZQ/D8Zk2fAq2lEfOGB6GoxgrSUnqoYJUye3PyzlGSi62J2WvS44ia0iZ6aIt5zFdxWjJw1UwkJfrDRSkrPZIMbTVp2T75EyfrCHnmax4WK6o8fqz2g4VxI6xkofpSLnigu1TsHwyhpSeHi9LCePhoouvFAMFF6Vk2uJ4grPiyOcLlk/RlvMYrrzneofhVDBSdLFdKc9ctoXGmjN9So7PVGUGp+fDYHBfBwsurhJVV9OVktLFAGfOlO2sibKH5SlGinKd/hBnUewYL3tU3ACnJfTd6YpPxZUSZoJTSlSLrXIu25dzVxxFxpA4EJ+ILWMlD3eWrQN5F0/J/bY8UdwtOVLuOmeKfyYrouI7WpLS1AOzcR4We8Ug9jKG4JyszI29EOdM7PkYoU9sRcGW2Ks4fjX2hoveTPwEsWe5SlJvy2UhojnOCT9eJ2dPH6YdOg5ceikA71qeIh7xuXBBnIaEzllNMWrigU5ZoJxzrhYjHde4dFGciCYLLwCXLY6Tigp9tSkp1VMTAb2xKanTkNQ5f0GcZFTj8sVCXbx6WYKIpnHJojg1MY23zYvRnNRJR6U3ieqyUFWf0LlwYZxEROPtS+V6Vy1NEItoXLwoTl1C56xmoYA2JkQsIRXViOsx6uIaFy8Uyuc7AluvWBInGdG4cKEs/oX0XN8H2xftuPPmyWLgZYvj6AFOTZO/UzHB2ZwShZx4RHq2+oTgvCDAecWSGZxRXXDWxgVnU1Kqz+oaxHWtOvS9aGGc+Cycb18qC14XBgt4ZzVFqYvr2L4QUdJRjci8GLUxOX9En/HJFYvFjvMXxGlM6qxqjJGKStXaeWmpR3fefMF5+eI4mqZxzfIEuqZx6WJZdD13XozmVDi019B1mXI1JARnIgJXLJHrvWNZgpgu97s2rnFOc4yGpE5dXHrxeFRioi6hc/GiOLGILDICXLkkQSKqHTX2PF+Rjmu87bDYu2b58WOvOalTf5zYq4vrsGqVqOGmUq8rMed4x8nZ09u2aILZNrwsEvoPdhQxXKGvTlQ8do5a9OZcDk6L2utwwRPapOnzco9QE5/oED2xF7oNSrZQT8fKHnvHbQ5lHLqzDnsDKumGAZOyrXi+WyiRT3RUcH3Fyz1Cb9w6ZDFUFD2zjmlbtrVGbSYrouRqOFKvDOCpzgqWq1jTZ5Cp+OwYsenPCe1TqLIeW0csMqbP6l4Tx5MtM4BnuwwqjlBCJ8oeu0cterKObE+O24wUXTYNCQ32xW6h1D4RbN292G1QtBSbhkxGSq5sLU4Lzj1jFhNlj3X9JmVH8VxXgPOgbBmu7jXJmkL1HSh4tEzYtE859OVddo7YTFU8Xu2TLbunO8XWpw9VMFyfV/tE8TbcvuqYcmiZsAVnQC9+uVcovE8EOJ/rNigFFN/xkseeMYuurENXsLU5UhKV26IlPlFK8XhHBS/AWTD96jbk/mC7rifrsmvMYrLssW7ApOIqnu2S6z15sILtCbU3a/hsG7EYyLu0Tjq0TTkM5F22D1tMGz6v9MqW3VMBzmcPVag4/lFjb/+bjL2ujMOeWbFXOmrsGUybnuhEDg9LhmqxeMKP18mZnDNb935sDE4/vap7X7QlIcN0JZnDV7O0x0P9cEsqzBYtn3NWLqOzb5i6hOiIp4NkjqgmE0jXl+SKiiNKs4e3Cc9Vtn1J5vBm5ma2J5TZkiM98BFtbakAW3F80dRTgJK5m+kFmu7HsHU2zmhEAyXyWfGISD+9Hpy2N7N24XqS8FI+Hk7Hl0QiT9qFevDp2Aye18IZD3yiFEQDPfjXwlmyfWoCff+oLjhd9fp9kgpw6pr4JcR5TJ/Mxhn6BIhqIk91PJw/6dg7rz7FEteV5JyTSff+LT8MAwYG5OH/7ncB+Lf1U5Qdn9v3Fqta4btHbTYNmrzcY3BwSkgbUxWPm3YW8HzF5zbmALhxW56c6XPvgRLdWdFi3zYiFWSfOyR69vcE2vjfDCiRn9uYw/UV391ZYLLs8WBbmY4ph5d7DTYMmOwZE/LNYMHj9kAX/StbpO2XNucwA9304YLLYx0V9k/YrO83WdNn0DLp8EigiX/zLqF8fmGT2Pq1rUIUuXNfkb68y9OHKuweFX31F7srdE47osVveHx7h+jdf26j1LT79vYC2UB7/VDG5YXuCluGLXaOCLGkNyekmKLl8/WtMzgdT/Tox0seD7eVaZt0eKXPYH2/yb5xIbQMFVxu2y0691/aLLZ+eXOuqvc/WHB54qCQbDYMmKzuNWiflFp8E2WP7+0q4MzyyTe25SlYQi3uyYlu/M4Ri63DFi90ifb+Dw+UyJoeN27Po5TU6vOU4js7CkxXhNJ8cFp0+TcPmewetav68nfuFYryVwOffGGTEJtu3l1gtCS03ZZJm7V9Buv6TfZP2DzaXmGk6HLLLqlb8MXAJ1/Zkj8i9vaMHRl7k0eJvW8GsXdPEHvPHSv2zCNj76adBSHcPPWUbF1PTcm/EzxO3p4eTtWy+zG3PWXrydf2p6GW3Y/nCKvWNjTAJz8J3/kOf/LDNj757ga+u6PA755fw/oBk7ObY5RsER08Z16Mtf0mv3t+Dd/ZUeDT72rkH17K8Oifwp/c18rHr23krn1FfvmsNHvHLRbXyN7vcFFqvD19qMKfX1rHlzbluPv34bfvauGbH2jmcxty/O2V9TzaUeZdK5J0ZR1qYjoNCY32KYf3rkzxQEuJv7+qnk+tzXL/H8GH727hS+9r5utb8/zpxbW80GNwycI4kxVZUV5eH2HHiMX/d05Q++y6Rv51dYaH/0Rqrv3Xu6Q+3G+dm2bzkMUZjVHMoJbdBQtirO41+b0La7hxW4HPXt/Ix17M8PCfKP7iAakPd+8BIbEcmHCYl5Z98P68y9XLEjxxsMJfXVbH5zbmuPcPBOc3bmjmC5ty/M3l9TxxsMw1yxP05z1iuuwZH5iw+cCqFPfuL/GPV9fzn69meeCP4CP3tPCF9zTxre0F/uCiWlb3GlwwP07WlFXuMxpjbB4y+Y1za7h5l9Td++eXMzzyJ1Lv7xPXNXLbniK/fk6a7SMWK+qjuL6shF+yKMHz3UKa+dqWPHd8RPHbd7XyrV9s5tPrcvzjVfU80FrmvSuFWBRqEHZnXd65IsEj7WX+7xX1fGZ9jh/+Ifzu3S189f3NfHlzjr+8tI5nugyuXBJnuCi17BbXRtgzZvPLZ6W4c1+Jf726gX9fk+HBP5bacp+5vpHv7ijw4QtqWddvcM68GEVLYu/s5hjrB0x++/wabjpG7N25r8ivnpVm95jFkqCW3WjJ44ow9i6p40ubJfY+dGcLN/5CM5/dkOML181n+dOPwvXXSy27ZBJOO+2EHq+Tt6cP69PncrBoEQNDI4y7No4vckOuP7due0TXqu/N/nnasqUMDI/Med3zVXXL82htj9bm8LYaMseOvo62oa2hjmlEk9feSNsTwakhc883hDOIC/0Ecb4RW/XXwPnj9smbwfmTiL0zUkmW6Do0Nv6Mi2iYphAMLAu+9z0A/n1DMKcP5o9PVedVIjt0cNrhwdYy0xWP7+6QedXnN+QARCDD9Ll3f4nurMPz3QbbRyx2jNg812XQG4hy5C2fG4N51ReCedX3dhSYrHg81Fqmfcpmda/BxkGLveM2Tx6sMFhwq3P6r26Wtl/eJHP6W3cXGSmKvNWBCZHaerXPpHXS5pH2MuNlrzqn/2I41w3EH+7cKwIdzxyqsGvUZsuQxUs9BocyDve3lMgYHjdtlzn95zfMmtObHvcdKHEoI/Xytg5b7By1eeZQhb6cU53Tf2PrDE7Hk9prE2WPR9rK1ZpwGwZkrvtER4Xh4syc/iubpO1XN+cxHJ//2SNrFz8K5vQbB0zW9Jq0T9k83FZmsuzx/Z0yp/9CONfdmq/Wb+vNiVTVjhGbbcMWL3QbdGWc6pz+29sKqACnpxQ3bRcRkQdaSrPm9Ba7x2yePmxO//VwnWWjzOl/sEvESx5tL9M66bC2z2R9v0nLpMNjHWVGS261FuGXw3WWcE4fxN6Th8Vex5TNg8F60uGxd+O2/JzYe64rjD0RVenJOtx7WOx9fsNM7I2XXXj6aejslPn89JwqcW/qODl7etOUXt40obcXzj2XnYcGUTGPyYpHc0qnaMnKuaeE9CBCij5NSZ3Jis/CmgjjJY9Lz17O3q4hFtWIWGFDUkQYY0FGmO1RFVKcl44wXva49Kzl7D00xKLaCBNljwVpnawpK7pmIIwZ1QIhxYRGxvBZkJ51vaDtZNljXlonb/mkYyKZrJAssbItZItj2TpVEQHHUiDC6Ic4AyHF5qTORMVn0TFw1id1oauGOF1Jxc2aPvNfA2fO9KmJ6yIACkQjGhXHpyGhM13xWVBzFJyH+cRVqppufDyfVHGG9QSUFPVIv4ZPxsseC9M6GdOnPqFjOirIPhSRzNpAiPM1fRLgtENhzB8zzjD2yo4i/gZi77KmFEsNQwg3IbW2pua4z9lPX09v2/KtNmuf/oF26WXW9ptMlkXKuSfncHBa6LXDRZfNQxZ5S/FSuFd6UKiKz3dJpdYNgyZjJdkr7cq6dGVc9o5ZjJc81g+alGyf54N93ScOlvF8OVfO8tkyZDEUyEF3TDn05qQ661TFZ22fieH6PB3s0z/ZWcHyFK/0GUwbPtuHZU+4bcqhddJmsOCydTjcpzdwPMWPOsXWcE943UCwTz8W7NNPO+ybsBkpemwetCjYqrpP//jBMkopXuyW6qebhizGSiI/3RlIWe8esxgve6wfMCk7Ps8emsHp+IrVvQZZ02fLsMVgIO/dPiXS0rJP77Om38ByFU8dmtmnt1wl9NmKz44R67B9enfWPr1Iioc+ea6rQtn22RDQk/eMWXRnXDozLvvGbUZLXrBPLzRjFeD0lPikYCk2Dx6+Ty8+mah4rO83qTg+zwT+/FGnVAde3We85j59xvB5pc/A9hRPHpaPsLbfZKrsV2Ovc1rotcNFN5DWnom9x48Ve2PWcWPv8VmxlzF92LVLMlPfon36k3MhLxaTlUrPg8suA+D6FULjvDjIVDurOUZ9kBXl+CJIcd58oTletliyv8KsqCuXJEhHNS5YEKcppbMKKTSBJgSMppTOhQskcyrM4LpmuVAkL1scpzamc+78GPNTUjwiqks111RMsr8uWhgjMSuD6+plCeI6XLIoTn1c55x5MZqTEerjQh2tiQmhoy6uc9niOFEdrl4m87S3L53J/mpM6pzZJBlkngLbFbGF8+ZLlt4VSyQj79rlkpF3RVDh9rz5kj2oN0p9Ol2TjLymWRl5YVbdNcuF8nrpIqEqnzsvJrX+ohq6LmSkRAQaEkKdjUXgHXMyDwOfJARnQ0KnMSlU4Nq49Cm1cZ3LFsWJ6hrXLE9WfZKMBT4JcKaDYhfzUmLr+Qskw/CKxYLv2uWSqXb5YqGinr8gxryUTlSXWnBRXWjIjckgSzI62ydJojqCM6FLhmUqrGenkYxJ+7qEUKFjOtUsyXcsk8zDObGXkFyGMPbOPSz2rj1m7EmxDZDYazxK7F27PFGNvbq4LgVffuYz8jxvJvd+eBiA7pzQOkeKLqYj+c8FW5ELc9JtyeO2g1xtXwlNFCR32g7y2StBPnve8oM8b3lN8p9hKMi37ssJRXK4KLnjE2WPsuNXc9KLlmKy7GG4fjUnPczV7s9LTvpI0cP0JPe+aPtkTaFwlmzJK7fc0NaZXO2BfJDnXXIxqnneUtopY/pUHFXNvR8Kcu77cvJzsODOyr1XTAc56QXLZ6oiOe5jJRfXm8lJ78sJ5bWKs+JRtuVauYBjMDk79362rQUXz5dVaMOV+xHm3meCvP3xIPd+uOjhKaHDgtxn15N8diP0pyX2Thv+jE88xVAxtFVy74cKwocYK3mUg9z7nCU57VMVOd9oSe5jyGkIOQbDRQ/bVUyUxQ9ZU/xSsnwmy5J7P1IUnAOH+WSk6GK4ci+L1lFizz1+7GXC2LMl9kLeh+2rWbEnOEOfMDX1c5B7r2kzrKKAYpsImE7xiFZlmkU18LQZ5lssYFCFTLWQYSX559I7R0KW1CymVuQorKxENLzeDAssZNZFdILSVgQ13LVqjXOCNlVbkXNXWWtKVrVD1l44504E7L54ZIaNpmtz2X3RWTg1bS4+TdOqP2Oz2FvhdavXC2ydjVP+DhmD0sNHg56zem/C64ZtqtcNbWXO50GYaDO2ckTbkO0X3t+wqm9UV+h60EabYa7FZ8dAaGtwvfDaMT2kvMpnqjhD9mSVKTcTCxCwuSNU72vo+yOuG/gkZPYd7pOQvXi82AOqPglZhbPbhLbqGsJFiURmnosTPE7ehz4aFbZdYyMg3Hg94HvHIrIolYgKySKqa8SjWqCeI/zkkH8NAcdZRzjsAYc6GXKalVblgkcCPjQI31vXNBoTwnWuD/jQNXGdaBAYtQEnviFQmQnbNqeE+9+QEO52bVx43z6yTROPUi1d3Rjwr0MudXPA3W6YhTMZ1fB8+YIJOfZRbQZnyI1vSkrb+oR8riYunHFdC/j0+gyffg5OAp65PsNNTwc8/EQ04NMHHH9dE6IIyE8ttFWfwQmy/RXyx0OcGjM8/saqrbP49BEt2EIT3vrRfKJpM/zz+oQW2KqTiBDUFpQHLPRJyKcPfdKYjMzh4ns+oMlinPhT7pFoDMz4pBp7+oxP5ItCYq9+Fk79MJ8cK/Z8NaNxoB8l9kJ/UlsrnV8k8pY89Cfv8L5SkZ+dnQDsmbBwPOjJOpRsFSjn+EyUZXidD9RoDFfUaGarl3RMO9iuKLEULT9QzpF/I0WPouXTm3OxPEX7tAyfDkzYeL6cy3RkWJqzfEaLHhMVUZQR5RxFd9bBnaVG0zpp4/rQlZ2r0jJRFpWWXFU5x+dQRqYCLZOh0oqD7Sm6sy4lSzFU9MgYMsQeKboULFGjMWcpBLVMzlLO8QRnwZLPT1ZEkWaoIEPvnqwMjdunZuFU0Jlxqbg+A3mXnCl2jpdlOjJYEEWZroyD40NrgLNtagZnyZHphfgkwGkFPnEUndNCbZ3jk0A5p2AHPjHEJ8MBzp6sUEs7pkUhqGVyRlHGDPyZt0TNaLIi04Khgksp8IntK9qmZlR+XIUo5zhiV870GSt7jJcChaC8S9nxOZQNFYJmKyHNjb3pIPZGit4c1aYw9kJ/Hi/2CpZPTy5QzpmesdXzFQczDhVXiXJOoSBb2GG26gkcJ2dPH4tJD2/b8M53AvBrq2qIRX2uWpqgOVz8CKqjer5QMBPRBHVxjXcuTxLRND4Q6JS9+7Qk6ZhoyzWnRLkkHEItrhVixpVL4qSjoscG8IFAp+y65UnqEhqXLRatt7CnDFVSGpM67wgW30LdufcHemxXL0vQmBSqZm1cFG6Ukt6zNia0ymuWC+XzhkAj7/rTk6RiOm9fGqc5rXNBoKnmq4BCHBMdu9q4xrtWiEbeB1al0DT5uzZY+GpK6aRjMorRNFhYI2qtogWo857TZ3BGg4Wn+oTOpYviwaKfqg5XG5OysBYuaIW6c+9dmSIR0bh6qejqXbRQaMiuH5GtrKhGKlDPuXaFUHhDn1x/WpJ0gHNeWhZIE1FZyHM8Ia9cuSRBTUw08bQAZyTEGde4fInc39r4zJB7fkooxFctS5CKzuC84QzRArxmeYKGpM4lC4X23JySLet4oKbTmNS5ZlmCeGRG8/C9K5Mkg0XBObHny4gmFdNIHif2rlgSZ15KKtYmjhZ7Ac7ZsffO5UfRyPuZXcizLFHDtaw5arhlx+e5boOxYDsn3DLZMWLRn3NZ0yfbTlVF0v2iSPpoe1m2uHoMhoqyjRRu1WwdthguurzYY1C01Ywa7v5ADbezQsbwWdNnCM101GL/RKCGOyi0UKHD+jzQKte7r6UkFNRDFdk+GjBli2bcrm7Bre03ma74PNUplM97Q5XYoAbb810Go8H23MFgCyzc+lvda5AzfR47WBY13P2ihvt4R5mcJdtjgwWX7SMzarhbAhrqi92i+ltVw91fEmpvZ4VMsC3Xk3PYNWaxL9ja3DBgMl72eOaQgeH63B8o9z7QUhJKcZfBeNljw6DJoYzLvgk7oJ86vNov25ahGu69+2fUcGU7zmCkKNTUjimH1knxyWDB5aVeg7yleLRDtiTv3j+jhpszhQI7kHfZMWLTEqrhDlmihttlUJ6F84cHRA336c6KbLMOmPQElOO9Y5ao4QbbweFW5H0Bzgdby0eNvf0Bzv5cqIZ77Nh7KYi9bcNSNy+MvaGi1CsszIq9u2fF3pThwcaNUgfiLVLDPTmTcyxLhvflsqxcLltG98AwGd/BcH1SUUkeieoyR1YBXdX2pBcNP2O4PqtWLKNncJhUVMd0hXZpe6oqWeQF1VXD9w5vU72eK8kjri9LDpomvycix77ebFtjulwLZEHHOY6t4eu2J4knBDTOqA6WR9XWY+FMBLbqGqDJaOj14oxFxFYNae+8AZxVn7xOnEfzydFwHu16s3G+YZ/MwvlGffKTjL2za1IsAdGKDNNwT0ZqraZpH9I07QZN0/7tTZ3AMKCvTx7+r38dgL99ZYKy4/O9nUX6ckJN3TkiFWuf7arQNuVw5z6pZffVzXk8X/EfQW2wL24UeuOte6Se2JOdFTYNSbXSHx2UWna37pZadl/YKN+kn1iTxfUVX9uSZ6Lscdf+Ii2TDs91VXi1z2TXiM1DrWX68y7f3SFpuJ9elwPgU2slDffb2woMF1weaCmxZ8zmlV6Dl4Jqu/ceKDFWcvnmVknD/c9XxdbPrs9RtH1u3lWkN+fwaHtZqqMOmDx9qELHtMMde4tMGx5f3iTVav9jjdS0+9KmPFnD4/a9RQ5OOzx1qMKGQZOtQxaPdUgtu5t3SS27zwVpov/5ahbHU3xji1Br7zlQ4sCEwwtdhlRYHbV5oEVq2X1newHD9fmvtdL20+uEWnvTjgKDBZeHWkvsHrV5tc/khS6D1kmnWiX261vyOL6q1mv7/IYcBcvnB7sLdGcdHu8os3XYYuOgyZOdFTozUm8ua3p8caNQa/9jTRZPKb6yOc90xeOOfUXapxye6aqwfsBk+7DFo+1lenMO3w+q/35mvdj6yVez2J7ixq0FRosu97WU2Dcu1XylYq7N/a1Sy+7b2wpYruJTAc7PrM9VY68/7waxZ7Ou3+S5WbE3eZTY+8LhsXfwGLFnzsTef4Sxtzkv1NpHHoH2dpiclH8neLzlPb2maZcDq5RSj2qa9lFgp1Jqd/j+KWrtydP2lK0nX9ufVmrt7wIvB7/3ADcAu4/98aMchiE59/X18OlPw4038pf3t/HxdzZw864iHzo3zcZBi7Obo1Vq7VnNMTYMmHzovBq+v1NonP+yWqiRf/FAG/8cUE5/cVWKfRM2i4J6YqMll8sWJ3i+q8IfX1LH17bkuf0jQhv96vub+eKmHH99eT0/OljmmuVJenMuqUDy+GDG4d2nSe2zv72yjs+sz3HPH8Af3NvK597TxLe25/nDC2t5udfgooBa6/mwrC7CzlGbXzs7xR17S/zLNQ38x5oM9/8R/On9rfzHdY38z54i/+dtabbMotbmTJ9z58d4NaAQ37SjwH+9S+iq9/+R4q8faucfrqrn/tYy71+ZpHXKYV5KtqEGClLj7enOgEK8Ocedvyc4v/K+Zr6yJc9fXlrHU4ekZt9gwSWmy/ZR65TN+wIK8d9dVc+n1wkt9w9/2Mpn3t3ITTsLfOSCWl7tMzlvfoycKck8KxujbBmy+PW3pbltd5GPX9fAx1/J8MAfwZ/dP0M5/bWz0+yYQ631uWhhnJd7DH7/IqEQ3/q7ig/f08o3Arrz311Zz8PtZa4/LcnBjENDIC3dm3O5ZnmCJzoqfPTyOr6wMcddvw+/d89cuvPz3QaXLY4zWhJq7aKaCPsmbH4hpBC/o4H/XJvlvj8UGvCnArrzb59Xw4YqrdufE3u/dV4NNx8We38e0J3vOVDkl1al2Tdus7hKrQ1ir7vCH19Ux9e2Sux9+O4WvnaDxN5nrpnP8ueekKIvZ5whD/zJRq3VNO0W4Bal1G5N024APqCU+nj4/pud03cNDJM9zpy+Ogd0fFIxHcPxWXXaMnoGhuVvVySSHJ8j5lXVudjhbYJzva754zHavub88TVsPRynr2Q1/Xg4Q1tn43TVG7Q12L/WNXDfhK1CG5W57vF8Ul27mOWTWCApdrL75I3E3tFwHi/2zq5NsUQpaG4+uef0J3yYpqTfWhbccQcAn98qNcLvbykzVHB5oavCgXGb7SMWa/vN/7+99wyT4zivhU93T968i5wJEiTFLAaJFEVR0bJs89r3WrZsy7IcPsvXNzheS5YsywpWligGSRQhMeecIwAiZ2CRNuecd/J07q7vx6memV0sAgnSBCnU8+BZ7OzU9Hu63p6urnrPOehKuXiqvYBpw8Mdh+gFduNuPh7cfiCHjOXjsRadvmO9BhrHbBwYI1U2WCPIWj5ubySh4Se7s3B9gTsP5TGle3i6vYCOJP3Odg9baJpw8HKXjuGsiweOFKA7Pn66j31v2ZuF6XJFfjTvcs1hkivo2wbM4vP2RMHDPYe5qnzTHsb68/18Fn24uYCBjFtcA9g3SpzdKRdPtBWQMjz88mAOviBOXwj8Uj4DP95aQI/0kds3Shrwuh568T3SXCiuGQDAT/Zk4XgCdx3OY7Lg4ZkOSlAFawEtch1jJOfi/qYCDJfP8ABw674sDMfHA0cKGMm5eLFLR/MEV6W3yhXuZzooI3XXIXrm/USOyS8ac8hZPh5t4brIuh4DB8fpDRf46T3Rqsvn4RyExOkJgV8dJLX4ybYCuqQv4N4RC4fHbbzazZ2Lh5oKKNg+fiZx3ryHayfBGsNznTrapuh9t2PQLK4NjOVd3HskD8sVuFni/Nm+3FG51zTB3Ns8wB2Lp9tJ6z4q9xpLudebdoq51yhzr1fmXqYs926UuXfHoTwmdBd45RWgq4tS2MnkKV9eb8Wd/vsA1gkh1iuK8mnw+f4Hwd8/+clPipUrVwIAbrjhBtxwww1Hf4hp8nnetlmcc/HF2N46gEjcx2jOxfwKOogm5F6pKyhomDZ9zE+oGMl5WFYdwmDWxfvOW4497YNYVkXqYkNcQ872i6WVlse90inDw6IKDUM5r9hneXUIw1kXi6s0TOo+aqMqDFcUS3F1h86oEwUPS6pmHm95dQjDOReLKjQkTbrI2h4AuU+ftXw0JFSM5TwsrT6672jOxbwKDVmTgpy+oOhjIqIibfiYX3E0zr3tg1hapWGi4KMuTuHIkKzIM13u00/pHhZXzhFr1sWiKg3TuqSruqJYJpx3BOpjKsaPgXMk52JhhYaUSZFLx+esJB5SkDkRzryLeQm6Asc0utYG+/RJw8PCOcZkKOtiSZWGyYKP2jgFOYOSVtMRqI6pmCp4WHysManUkNQpYGm5oliGnLcE6uMqxgoels7R95i5F1KRtph7o3PgPFHuTR8D53DWxVXzEliaywGLF7N2JRplhd6Jr8P/0jv9IwBWy/+vBrC+/I8rV67E2rVrsXbt2rkveICkgnSaFXk7dgAAXuylQ+qeEdIfmydtDGU99KZddEzTy+zgmIWcLbBjyIQnKCEMAFsHTOiOKEpWt0076M+4GMi6aJ1yMKV7aBy1obuUZAZQlDLeMWQhZwkcHLMwVvDQMe2gJ+1gOOehadJGyvCxZ8SSFFP2fU1SM3dLWukRSYntSTnoSjkYzbs4PGEjK6msji+woZexbu43YTg+9o3aSOo+WqYcDGU99KVdtCcdTEq6bUHKKvsSpxD8Pe8INEoZ6LZpB/1pF4MZFy2TDqZ1D/tGbFJ3+xnrekl53TFsIWv5ODRuYyzvFiXCh3OUw06ZPnYPW7A8UmkBYGMfpaJ3Szlv0kyJszPpYKxAem/O4ucHss4AsGWA1Nf9o5TXbp1yMJB10Z9x0TbtYFL30Dhmo+AQl5A4vQCnLXBgnLLeHdOkAA9lPTRPOUgaPvaO2jDcEs4NvQYcX2CXlKo+PGFjNO+iK+WgO+kUKbppizhtrzQmm/rNOXOvR+beeFnubT9B7rVOMff6M6Xc2z9qQ3eOzr3tQ5RfR3NziXRTKLzR67LY3vSFPPksf6V8nk+Xr9yfdNM0enD7PrBmDQDg0vmkca6WVNNl1SHUROkc6nisplpZQ8rsmvowNIX0VAA4ryGMSEjBWbUhVEVVLK7UkAizFjwmDQ5W1YYQ1Wj2AAAXzSdF8pz6EGJhBStrQqiNqtI2KyBhhFARUXB2XRghDXjPPPa9YB7psmfX0QBheXUIdTH6nwlBCuby6hASYRVr6kMIKcCFMtb3zAsjojHWyqiCpVUaqqJ05632VFTLWGMhxqpKnIpCA4eYpmBVLc01llSFirX3EY019GfVhhDRlGKsF86LQFOANXUhJEIqVtSE6M0n75yxkAKBECrCxBlWgffMC2IlznPqaGixvDpUrAT0BPkFK2pCiIcVrKkLQVNQHJPzG0o4qyIqllZpqAyr8IU0EYmoWFVDavB59WEoCumpmkLcsRDHpDqqwhchRLSAtMPa+LNqSbc9X47nhfMjCCnAOfU878urOZ4BiSgRVuDXhFARJs03pJaNSUN47tzz6JhccxK5t0rm3pKqUu7Fwwoq5XhGQkfn3pp6ScNdtox392j0TanIe0vKcIUQJ1ipO+EH0LFW03jHBzBleFjmh5C1fDgekLcFYpqA5fFfPKwgZwt4Ple5hRBImrQJSps+fB/I2j4cT0B3BFSFiikFW6A2Sjslz+d7ASBpkiKZsXx4vkDOFqj3BHTHp+Y5gILjw/E1ZCwfvijra5Aum7V8uB6Ql3rphiPkYpyCvO3DlbH6sg8ApEwfnghiBQqOQFgTcH0hNeQV5CwBV8yB05J9LQE7IVCwfYgwSUgFR8D2BXI235MqxwkgYzGevFT00R1RZB7m7Zk4g74p04cQ7Ov4KGq7G66QC2oCOfm5GcuHkMcLxsST58jxBPK2QEjl+Sk4AlVRGatPXMF5FRK35wvkJE7d8eELGlgWbN4EsrNiTRoBTlHEWR1lrAB5LMTJXBBi5pj4vozVn5l7gfdBzhal8RSkb5fnXm5W7kHmXo3E6R8r9wSoIuW6nPn6garfG2+nZ+29ECVwNokLppSasj0BX/AEu4IroK7Ptzs+k8aW77XkgNqegA8mgydr2AOBQtenl7rjo/j5kH35O4p1754QxSo3z+dqry8EHI8laGbxeKXP8oEZx/UF4AlRFitm9C0dVxQ/2xflxyNOIfhMWOwjmIBCfnaAyROA8EXx2LaM1So7HmQcfnBc+X5AKZ5fMcd55XGDWEvHC6zGApyMFTP7ejP7umUxBuNpe4AQYmaf8vNa9v5gXPiaPL9l42kWcfK4wTkiTsD3FXm8Mpy8bmceV+aeV5Z75TiD45X/LM89x2PuASgbE8CHmJF7wU9fgBe86868Lk6hnZ4XvaZR8VMITm0AnFPLKdeSKk635yU0qZyjwAnTT2xhhYZIiNMvVVGwqpbTpeXVnOotqtSQCJP2GCjnhFTSSBdXagirfC8ArKrlNG1pFckgCyo4/RRxFJVzBDTEQ5xGayqwqpZ9V9Zwyr6kSkNMU7CgQpX0VKWonLOwQkM0pGBZNSmfQawrakIIqcDiSk4X5yU0qZyjIB4WSIQlTo3TaUXiVBT+HtYULKrQUBFWMC+uFpVzQiotrxdXhhDSeJwiTrWEc2GFhoqIKrfrSA7xEiwTXVpFS+6VNSWcmgosqeT5XFChoSqiIqoxsSsDnJqCZVX0cSsfk7AmccrxDJRzohpxLqqkBXYwJmfVclyXVfMRZVElcdbH1aJyjgIN8bDEqc7EqSqskYjKWCsjqnTKpXLOAp96hEskzlVlOIPci4dUzEtoqIoqiHvMvYqIOkfuhebMvXkJmXsgLTfIvYiqzMi9AGdUU+huU1VFIlpg4X4K7fTcsnOcEpWwkUsCmwapz3Z4wkbG9IsLRYNZF71pF9O6h5ZJBwVboHHMlotwXBjZN2pBdwWaJ20kDb+4QBUsrqUMH00TNgxXYO8oqwF3DJnwfIEDYzbyjo+2KQdThoe+jIvBrIvxPBeQMqaPw+M2F7SG2XfXsAnbBw6N28jaPtqnHYwXPAxkXQxkSHdtm3KQs30cGCM9daeMNVgUbJqwkTZ9ufDnYTjroidFSmfLlIOCI7B/1IIviNMXgjgd4pw2SNkczrkYzXvoSjpImT6OTNowXYG9I4x15xA95g6M28jbfnERrU8uAI4XPHQkSWE9NGHD8YBdEufuEQu2B46J5aND4hzMuuiTOFunHORtH41jNhcMJc69IxZMhxTUlOmjK+lgNOdxITDtImn6aJm0YTjEJYTA9iELnuCimG4LLk4apEUPSZydSae4eGrJxbcAp+sDB8Zs5CyO52TBQ3+G4xIsCObkYqbjcxwBFBcwZ+RevpR7wUJkee5tH7Jm5F6w6NudcjCS9zCSZ+4lDR9Nk1xEniv3crbP7brJSRatGcYpX16nJ+EmUMO1bZpenHce9ncOwi9Tw81bR6vE5qxZiqSBuugbUcOVfV6XGu6sviejhjsVKK/O6nsiNdyGOGObE6fhoTo6Sw3XAyrDc6jhzsIZqOHOVomtjqrHxvl6VGKPhfNk1HBnxXo8Ndxj4XxdargnwOkJTvNPBucbzb2iGu7ixaXinHelGq5lAaOj/Fa7/34AwI/2plBwfDzRWsBIzsP6PgPNkzb2j9rYPmSiJ+Xi+U4DScPH/U0skPj5PhZI3HM4h4zpF33ONvebODRh4/C4g839JgYyLp7u0JGxfNxziAUSP9/HAokHm/KYMny82GWgK+Vgx6CJ/aM2WqQG/kiOxTC61H8HgNsbWZzzSGsBY3kPr/YYaJtysEd6tXVMU3t/Qicdl3rsjPVOqdf+ZJuOoZyH1/oNNE2wkGjroIm+tIvnOnQkDQ/3HSGl9mf7WJxz35E8UoaH5zp09KVJiT0wbqNpwsHGPqPoN5ezfNx1kLHetp/FOQ815zGpkz7amWQh0d5RC21TNtb3UMn1sRYW56xtZKy/PJCD4fh4rLWAsZyHdb0GWqds7BuxsHOILrQvdhmY0n082MzinNskzrsP5ZC1fDzdrmMg62JTn4Ej43QR3jJAnM906EiZHu49nIeQOD0hcP+RPJImFX17UnS3bRyzqdffZ2Ao5+GJNlKU75A4fyH9BR5qyWOi4OHlHgMd0w52D1vYM8IxeaWbFOFHWgqwXIHbJc47DuRm5N6GstzbMWiiO+XghS5SiIPc+9kJc4/ehsXcM4/OvQea8pjQPeC113i3T6X47xTb6XmnDxxudJ0VSKeTw43gnYFSW2+9w82JnF/ebIebIK4zDjcn6XDzBnC+IYeb+vqSiMa70uEm8LIzDODb3wYA/OUr4yg4dGbpS9O5ddewhQ29pGI2TdhY20hq7Te3pOH5Av/0KksWv7YphbTp46d7s2ifdvBYawFbB0xsG7TwaCvpjbfuJbX23zfxm/SfXk3C9QW+tTWNiYKHXzbmcGTCxrMdOtb10KXk/iN0ofnRzgx0x8eXNvB4/7I+CdMlBXQoS6fY/aM2Xuk28GKngQNjFu44SKeV70jnlX9ex75feS2FnO3jpt1Z9KTohrpjyMLGPhNPtetonbJx2346vHxjC51t/vHVJHwh8B+bU0gZHm7bl0XrFN1mN/Wb2D5k4aFmUmtv3k1qbUDl/ed1STgenWfG8x5+dSCHQ+MWnu/Q8Wq3gX2jNu49TGrtD3dkYLg+vriesX5pQxKG4+OHOzMYzLq470gee0dsrO8x8HwH3W5+dSCH8YJHJx2/hPOrG1PIWj5u2ZNFV9LBIy0FbBskVfqJtgLapmz8bB8de/5jcwpC4vSEwDe2pDGte7h9fw7Nk3QPfq3PxM5hCw82kVr7E+n+G1Bc/9+6JGxP4Lvb0hjNubjzYB4Hx2281GXg5S6Wxt59iNTa72/PwHIF/kXi/PJrqWLu9WdIy909wtx7tr2Ue5O6h29tZe79o8y9fy/LvY6y3Ns6YOLR1gI6pmXumaXc+8ey3BstuMCDDwJHjgDj4xSXOcV2+t7pgTPU2re475lYT7++71Rq7am3QESjpgb4xjeAH/4Q/+uRVvzTNdX45YEc/vt5FdgxZOLs2jAKjo+8LXB2XQg7hiz83nkJrD2Qw5euqcGXN6Zw358Cf/tIC/7ufTV4qDmPj58Vx5EJGwsktXYs7+HShRG82mPgsxdX4qbdGfziM6SNfucjdfjhzgz+6rIqPNep4+ql0SK1tjqqojPp4IPLY3iyrYAvXF6F72wnNfIvHmzG166rw0/3ZfHHF1TgtX4TF80PY0pnocqSqhAOjFn4zbPjuPdwHv/w/hp8bXMK93wW+OuHW/Av19Tg7kN5/M6aOPaOWFhZU6LWntdAh9Tff08Fbtufw1eurcG/vpbCPZ8V+L+PteF/X1mFR1sL+PDKOFqnbNTHuRU5lPVwxeIIXuwy8PlLKvGjXRms/SPgz+5vxn9+uA437s7gzy+pwovdOq5cHFBruR3WOuXgwytJIf7bK6vwra2k5f7lg8346gdr8YvGHD79HjoJn99QotaurAlhz4iF316TwF2Hcvjnq2vwb3JM/uaRFvzT+2tw75E8PnV2HAfGbCyt0uD6wJTu4cL5EbzWZ+AzF5JC/PM/EPjc/S343sfq8L3tGfzPy6vwRJuO61ZE0Zl0UR1VEA+p6E07uHppFM926PjLy6rwg50Z/PKPSI/95vWS7nxxJV7tMXDZwgjG8h4URcH8hIojEw4+flYMDzYX8H+vrMbXt6Rw92dJj/3ytTUzcu+cuoBaW8q93z0vgV/Oyr3/+UgL/v59NXiwOY9PnBXH4TJa94zcu6gSN+2ZmXs/2JnBv7+/ActeeZbU2pUrecEvX35Kl9fpe6cvFPhMPzYGrFyJ1t4h5BUXuaC6zRWIaCSi+IKa5abDPdOcRTJF1vJx3qqlaO8bRnVULVaMWZ5ASD5YuUIgqrFirSpydJ+sxRXigk3ii+OxCERVUKzGyttizuMFcRQcn/vd8iEwJGmjFeFjxxrgNF2BkKaUqLUaYDh0jwliOyFOhWSdWEhB/hg4i7HaPmIhOgdBIeXU9khoOmas8nXdIZmkiPMkxmQ2TojSmOhlOE9mTJTXg9MhwSfAGVJOfkze7Nw7Hs4LquNY7LqlvfpY7F1MrR0bYxXSww8DAG5qTEN3fDzVpmMk72FjH+mQB8Zs7Bziau9L3QaShoeHmrmCulZSFe9vyiNr+Xi+U8dg1sO2AYpbNk3a2DpgYTDLFe+c5RcFKtceyMH1BZ1wDQ8vdxvoSbnYNWyiccxC65SDjX1c1X6qvQDD8XGXXH294yBdTx9vK2A872FDL2mm+0a4UtyVohjipO7h0VZ6rAUr//cczqNgU0hyOOdhU7+JlkkHh8ZtbB800Z8mhTVtUqDSF8TpC+40ZEwfL3RxpXiHdNdtnrCxecDEUM7DM+068raPe6Vw4y8P5OB4Ao+00HX11R4DXSkXu0cs7B+10D7tYEOvibE8Kb2mK3CnXBG/8xD9BZ9sp9vra32kDTeOWtg1zB2VV3oMTOseHm6hZ95aifPeI3nkbB/PdXCXYsuAiaYJG4cn6AYbOPZmTB8PNHH1fm1jDp7gTkPK8PBil4G+tIsdQyYOjtlomaTg6EjOw9PtOgqOj7sP83i/OpCD7Qk82koX3XXSAXjPiIV9IxY6kg7W93D1/rHWAixPFFf+7z6UK+be6Izcs7BzyERv6ji5d4S599ys3DsyUcq9ZzvoQXh/kHuNpdyb0F1g0yYKY6bTxbL0U2mn5/Q+EuFqpesCn/gEAOAz51UhHvJx/coYFiQ0eoRFJL3RF6iIKIhplDcOJIR/77wEAOA3V8dRGVFw7XL2TYRoUKAAWFpFf7jrVsRQEVHwqbP5Lfp75yakZDNliK9eRpnnemleEFY5JWyIa7h+ZRzxsIrfWcPj/bdzE4iGKBVdn6DMc3VExeJKlobGQwqqIlHUxVR8bFUMYU3B78pYf+uceFEOeUGFhsulF5ovANvn3esD0vDik2fHoSrEqSoKfmN1HFVRynbPS7CCMCIJN4urQqiNqfjQihgqwgo+dQ5x/u65CYQ1BR87K1aUua6NqZiXUIsOMfVxFQ0JDR9ZFUcspOCGcxnrDWsSUmY6jnkJDVcuph+e4wv4cq89Eebnffwseub9d4nzU2fHURlWcJ3EGdGiiIdIrbVdzpyuXS5xSonv3zsvAU3irI6p+MCyKOoTqjShUKCpwKIKDXVxlRLbIQW/fU5pTCKago+tiqEuTtny6piKBRWc6UZDNDZpiKv46KoYopqC/yZx/vaaBOIhBdevjGF+QsMVEqdblnvxECXSj8q9s5l7H5S5Fw8pRfekZa5ATZS5VxlR8JtB7p1Xyr36mAZcfjmwaFFpn/4U2+l5p3ddFud4HnDwIABg+7AB2wNaJln91ZVyMFGgMUJ/xkVS92kOYAscGqcpwm5ZjXVgnNV2bVMOUibpuGN5D6N5D71pB2nDR+sUDRQOjLHWf88Iq78Oj5Pe2THN6q/+jIvhLI0gulM0ZWieZEXePllRtXfEguPRbCNv+ehKsjptMOthMONiSmdVV8EWODzhwPVL1XyNozYsaZyRMX30pFh5OJJ30Z92kTQ8tE87MByBg2M2fIlTCIGD46xga5t2kJLVgyN5F2MFVn9lTB+tUzZMj5VjAU7XJ868TbOGaYPGD0PS2KMrSaOGpgkbtleq5ts7Qgpq04SNrOWjK0Wcw1lWuU0ZrNLLO/x8rwzngTFWBrZMsvKwN80qt9Ecq/lSJqsWDYfVgkLi9CVOXeJMylhHcqyS7E47yBTHhOczwOn4AkcmnCLOKZ1GHkNZj2OS4uPjkQkHThnO/aPWjNzrTrFS8ajcc+bIvTHmXuucuUfDjdm5t1vm3iFZJYmeHt7h36SKvNPzTq+q/EYTAliyBACwqiYMTaWWWaxYk84673iItdrzE6xJX1wZggpghaxlXlKpIayyBj4eVlEXF6gM87lKVVirvSDBu8WSKuqXLa/mZyyuZJ13UBteF6d9UVRT4MT5/LiwQkNIAZZVleqtVXnXiYQUzEuoqIioUBQSYipkDXYkBCyuZO19UCO+tFpDKMAZVlAfp9ut6wtEND5bz0+wJn1JFe2PVsga/CVVfH1+gvTNehmfpgBClOrjQypr4YuxKqwrj4Qg+0rrKEWR9f+sClxUyZr0oEZ8eTXpsosqyTFoiKuoDKsIqUIaczCWaDAmZX2XVmkISU5DPEQ+RGVEgRAKQiqFKRZUEM/SKtpZrZB17UtkrfqCilKsUU2RdRQojYnK8wnw/AaxRjXImZACgH8vchU01sKranmsodKYlOVe5GRyr4q5t1DmXv2M3FNZ8z8r91aU5V40pHDWG4+/abX3p+dFD/CCV1Xe9UFWFCBZYwLwJJsqWEzxwdcEUCwsccv68PeS1pwkkcEPPo8kLC7slPV1hYAAjyUk201VyK7ziscN+pYdV7LpIMqPy88o9hGz+sz4rFIfX/CxgLGKGZ87V1++n2W7vgiKVkTxuHP1DWIuP0cKBHwoZbHO0SeIFaXzGvwrnlcZs5jVJ9DyF8HYCUWyECHjF0eNiZBMR1H8vfyYZeM0x3gGuTEzVsbjC6XYZ678EeU/ZRyzc8+HOKpv6fizcg8nzj1PYiky696kRffT86L3fZJuNK2oCTauezhXUJLJ9gWyto+4XPU1XX7bktctMK2Toz6pkxs5rXtFrrPlkUutKnyyycp6/YCjHfCgJ3VP8tzJiU+bPuYlBAqOj4ivwBdKkQueMmltPGX4si+53ElDxipXm/WAT6+JIgc9ZfK9kwX2nZKKuWnTh+0JZC3e4V0fKNiU3Uqb3PpLGuTTT+rkmU8bJY6+5ZKnLaAipKLIPU+ZPlwh6JwicQoZqyM54w1xVfLbAUURRR2ClEmdgCk9iJV877TpwfGodVAR5mq04wMxTRQ56Iy1bEwMD65gPLZLvYKAT5+3KU2Wllz8aYlvQvfIyTdKHH3L5Xh60qosa/mYnxBFHvuUPN5kwS/h9KgBUCu5DQoATRFFrYakIcdELxsTwbGyvZm5Z5XlnuujmHsT8rhJY2bu5axS7uVOIvccXwC5HKf1nle8CZ5KOz0v+lCIJYe+D5x/PgDgigVRRFSBc+pCqIyoWFEdkospvCColkKlkfPnkRZ7yYKSwks0pODsuhCqpRpNjH7KqIxwz/3sOk6lLpCqMJcsKKm0xMP87NpYacEorCpF59o19WFE1JIqzMULIghrCs5tCKMyTFWVmpiKyjDFNxIhBagNIRGm2k1IVXDJQva9YH4EEY0KL1URFSuqNSQiKnxfwI6pqI4oWF1H5Zjz55FSe8kCKue8Zx5fX10XpvMqFGm1TVptdUTFOfWka87AqZZwrqqlyk+0THEnpIRQIXGGVOAieV4vWhBBWAXW1IdRIVVyqiMqqqJyIS+iYBWI87wGUniDMblgXgRRjWNSFVWxrFpDIqTCBxe3qmNU6omFFFwglYEuXRCBqhB3PMQxqYmpUFUKaGiqUlRCOqee1N1A/eaShRGEJM5EhKo7dTG1SHONhRSoChWCzm0II6wquFjGeuH8CCIqTph78bLcu/QYubeseu7cixwj9yrCKunldXUnXYJ7onZ6LuQ5DokFpgls3QoAeKa7AMMV2DVsIalTz2wg46I75aJ1ysZY3sP+Ueq8bR0gNfHlnpLGmW4L7B2xMVHw0TzpoDftoC/toGWSVNI9IxYKjsDGfvZ5uYfacVsHTGQtH41jFsbyXETrTpJee3jcxrThYeewBdMVWC811db1kAa8fZDacYfGbQxlXXQkHXRMk9Z7cIwLddsGTTiewCvdOgDq6xkuF7ymDA9HJh0MZFz0pCXOgod9oxbytsDmflJqX+4x4Av+nrcF9o1YGC94aJmy0ZPmYlOTxLl72ILhlHTuXumhdty2QRNZ00fjqIWRvIf2JPX8hnL0pksZPnYOWbA8YJ3Eub7XgOUBO4YsJA0Ph8dtDGZddCWpczea89A4aiFj+dg6aML16ScY4NQdUl8ndQ9NEw76Mi760i6apzhOe0aIc2MfNfJe7qZG3uZ+E1nbx/5R4mybstGTIm35yAQ193YOWTBcgQ1FnPQM3DZoIm36ODhGPb+OJPX8hnMeDo6T5rt9kFTaV2WsG3oNmLNybzDL3GubJvV5/5iFXHnudQe5ZxRzb3KO3JsoMPd0W2DTHLmXMn2gqQkYGWHtSj5/ypfX6VmcY5oEaFnA4CCwejWO9AzBVLnaWR3lFDKqBc+ApQKb6qiKlOmhLqYhZXi4YPUytPQOoS5GuafKiCwEUWWBhCcQC7PApkb2veCsZWjpGUJdXCt+VjB1tT0BReHimOVxsSpjURW3eDzZN236qImyUIQFL3x4C2uUzqqaK1bZN2P6qIryfWFZnPNGcSqgYktcSm3VzBFr8Fk5i1NXJ8CpUnWm8mRxyuIcIcTxcQaxzsYJPtPGQic/JpYnoCmcmVgep9vHw1kb5bQ+HlaKa0UhVTkpnK8794LxnCv3ZuOcI9aLaxJYbNt0rQ108hKJE15n78zinKEhPsf88pcAgK/vmEbBYQHDYNbDi106Do7b2DVsYmOfiY4kfd+mdJJjPF/gh7voDfbzfTmkTR+PNOfRm3KxvsfAvhELjaMWXu1lgcdDTXlkLPqVAcAPd2Xg+tSSnyxQY71t2sHGfhM7h0wcnrDxfCcLS+49wuKNQLv+xt2k1t59KIeRPAt/mmXRyZYBFnY81a5jPO/hzoOk1v5Ixnrr3izyNgtSBjIs+jg4Ro31Db3U93+0pYCkQcKJLwR+sJOedr/Yn0PKIAW2O+liQy/93Q6MWXi5m7r3DzTnkbN83Cqpnz/clYHjCdxxkHrwT7UX0DblYPOAie2DLJh5roOFQvccZjHOTyTOm/ZQ9/7ewzkM5zy80KnjyASLpTb1s1DnyfYCJgoe7jhAam0wJj/bS2rtQ8159KVZxNM4xkKZ9T0shHqkuYCU6eG2fdS9/8HODDwhcHtjDtM6Kc2dSQev9ZnYPcJCpJe6DQxmPdzflEfe9nGL1K7/8W5Sa+86mMdYwcMzHfQi2DpgYfughZZJkqlG8x7uOsTiqkC7/ua92WLuDcncOzQr955om5l7P9gpc28/c+9hmXvregzsH5W518Pce7iZRVWBRv8PdpZyb6zgAi++CLS3A9PTp6fu/YnaSZfhCrmAIQSwYAEGBwehKAqEEDN+AjjqtfKfy5cvf919j9fnVPqWtzcr1rcK5zsp1nc7zmWRCGuMq6r4811LuOnp4eLFl78M3HorPn9/K752fQ1u3ZPFH11Ygc0DJs6tDyNvczX1vPowNvWb+KMLK3DTniy+8aFa/P2r03jiLxT8+YMt+NcP1OLOQzn89jkJHBizsKiSpIfhnIerlpCg8f+9twrf2ZbGvX+q4NN3N+Om36jHN7em8X+urMZjrQV8aEUMXUkHibCCmpiKtikHH1kVxwNNefzD+6rx1U0pPPRnCv7o3mZ876P1+OHONP7y0iq81G3g0oX0snN9YHm1ht3DJAf9ojGHr1xL77PH/lzBn97fgq9/qBY/35fFp99Tge1DFlZLL7uk6ePCeWGs7yU56Me7MvjPD9fh716ZxmN/TmLIv1xdg3ukZ9+RCRvzEtwn7s/Q4+3JNh3/8/IqfHNrGvd/TsEf3N2MGz9Rj//clsb/uqIaT7UXcPXSKPozbrE+4bD0eLvncB7/fHU1vvxaCo98XsEf30tiyE92Z/G5SyqxrsfAhfMjSJkeTFfgrNowtg+Z+P3zK/CzfVn8+3W1+MdXk3jiLxT82QMt+OoHa7G2kZ59u0csrJBedhO6h0sXRPByt4HPX1qJ7+/I4O4/AT59dxNu/mQDvrYphX96fw0ebC7go6tiaJtyUBOj9HZX0sF1RX/Banx9SxoPfE7BH97TjB99vB7f3Z7GF95LAtWVi6MYznlQ5f5945iN3zonjjsO5vCla2rxpdeSeOTzCj57XzO++eE63Loniz++qBIb+wyc1xBGTvoorqkPY/MA/QVvPlbuHaRn3/4xC0ukl91I3sOVi0v+gt/ZHuReE276jQZ8Y0sa3/ngPCx77nHgwx8GVq3iBS/NYt5oO33v9KbJO302S2rt8AhGHVY7aQrlo1T5bSjAFergb+U/ly1ZgqGRkRmvB30BFP9/oj7Bz+B8KWWfc7LHO9W+bwSn8jbF+kb7vpExeTfjXBmLYXEoRFptUIb7rhXR6O/nKv5NNwEA/nHTJAqOj9v35zCQcfFEm479o3xGfrmbMk33Habv3E92ZeH5ougX/4MdGWRMH3cezKMr6eC5Dh07h0zsGjbxbIeO7pSDOw7wmf77O/gs9h+b03B9eq9NFjzcfySPlkkbL3cb2DxgYv8ovdAHsy5u289n+m9Lz/dvbqE//c/2ZjGSc/FISwGHxi281mdifa+JIxM2HmwiGecW6bEW+Kh/dxvFH37ZmENfms/+e0csbBu08FKXgfZpB/ccopfbj+Wz/Nc20Z/+RzvpT3/3oTw6kw5e6DSwfcjC7mELT7fTS+2X0kPuu9tLOB1P4OY9WYwXPDzQVEDzpI1Xewxs6jdxYMzCoy0FDGdd/Hwfn+kDb/v/3Ep/+tv25TCUdfFYawEHxui592oPJaXuP8Jn+pt3Z+GUjcn3t2eQtSgx1pt28EyHjt3DXEd4oZNkmLsO5pEyPfxwB/3pv7aJ/vQ/3kV/+nsP59E+7eClLgPbBi3sHbHwVBvJRrc3UnbsO9t4vG9soVjJrXuyGMu7eKi5gCMTNtb3mnitz8ShcRsPNxcwmnPx0730p/+mHJNvb0ufMPfunZV7X5OCGOW5150q5d7OIRPPleeeOUfu7crymf7JJ2nvNjXFf6fYTs87fbB6bxhcvT/nHBzqHoSteUgZFBgsSMFIT3BPOBpSaB4QozdYQ5xihBedvQxNPUNokKuh1RH60YXlCqrjcxWXRToUlbxo9TI0dQ+hIaEVP4tCilwpVhVKJFkuyRYZ00dd+fFk36RB0cecLQUjZVVYWNIpq6WAY/0cfVOGh2oppBgJVu/lam/O5urysXCmTR9VcqVYUxUoRXpsGc5Zx5s2PNTHVGRtvs8JBCNVUkmDoqC5Yk0aXrHQJRaMieAev36sMQlwml6xcCnA6folA4kA51xjkpYegVY5zpMck2PhrDrBmByVe4IuucfMvVk4KVZ6jNybY0wurU1gsWkCCxZQX+Jdu3pv25QFcl3guecAAHce4UrxK5L+uHPYQmfSQfOEg8Yx7ptu6jeQMrla7vkCDzbT9+upNtJmX+s1MZL3sHfEQtu0jbZpUitHcqS/5mzSJwHgweYCXF/guQ4dKcPDpn6ufh8Yo9BkV9LBjiGzKLJouBSIBFAUVnyxy8Ck7mP7oImeNP3rDo3bRdHKpOHj+U6DwpQt7PtEWwEFx8ervQbG8x52DVnonHbQMknn2sGsi439BsUW23X4QuCBZlJsn2mnuOdGKQ65b9RC65RdFIAcy3lY32OiYPt4QuJ8qJmU1xc6dSRNH1v6Sd89MGbjyAT97LYPmpjUfbzcbRQFPwHg0VZSbV/uNjBZ8LFjiCKRTRMODo6xjmLLgImk4eH5Th2uL/CQHJMnJcV3fa+J0ZyHPcMW2qccCmuOWhiSApSBeKaQOD0h8GwHqcWb+in2uV+KYnYl6Zg7lvfwSo8B3fHxeBuP91BLAbYnigKW26T45qFxG4cmWM+wbdDElE4RVEvSjQHgsdbCsXNvlDhn594DzdxPD4RIX+sl5beUe/bRuddeyj1P5t6U4QG7dtHFOZMpqUmdQjs9F/LCYTp0ui5wzTUAgN88qwLRkMCVi6Ooj2m4YB690lyf7iJVURWXLoygKqLimmUxaKqCj67is88Hl5OG+95FEcyLqwhJLzQowPyEirq4issXRZAIK/jgcq6MfnRVDCFVwTXLYqiMqrhsURTzJKFEU3m3ro6qqItruGpxFDGN1EsA+PDKGCIaijTVixZEUBtVUR9XIQQ9zCKy/9VLowhrCj4q+163IoZ4SCHOOHFWRFR4gg4oNVEVly2MFKnCqqLgY6tIsb12eQyVYQWXLYpgfkJFRAvLyjpJj41ruHxxBPGwgutWlHCGVQVXL42hOqrikoURNMRVVEVVqArvYhURFbUxFVctiSKqAR9eUcIZ1YD3LYmiNq7iwvkR1EQpK+0JklhCKivkrlnK81k+JvGwgssXRdCQUHG+Ei6aXVgu7/CXL4qgIqzg2mVRKBKnpij4wDJSUS9dGCkSdsKagpAS0GM1XLUkiliIFGUA+OjKGCKagquXkgJ78YII6uKqrFxkRV6wQPv+pVFEVOIDgOtXxhALxiTIvSglzYOKPHVW7n1sVXzO3NMawsUqwPkJcczc02Tu1UZV4IILKKIRCGOeYjs97/SeR9UcISj9C+DIlAXHB/oyLgqOj5Gch6TpYcrwMV7wkbV8DGa5atyVdOALUmkBoDPpwnYF+jMucrbAaN7DtOEjafgYzXvIW/yb7Ql0Jlnb3DblwBMC3SnSHgcyNHwYL3iY0j2kTR/DOQ+6TbMFxwfap3m89mkHrgB6UqRbDmVdpEwfkwUPEwUPGdPHUNaF4Qr0pB14vkCr7Nsx7cDxgL60i4LtYyTvIWV6mNZ9jOc9ZC1SSU2POIUgbVMIgc6kA9NjrDlLYKyI08NozkPe9tGXdmF7PA4AtE7x+N0pB6aMNWP6mJA4U6aP4ZwL3SFOtwxn27QD1wd60/z7SE7i1CVOi9RV0+HnezLW4ph4PO95m7EmDR/Tho+xgoeszb9ZckwCnL4gbssVGMzyfHBMfCRNmkjkHeJ0ynFOk8LcnXKguwJDOeKc1EkfTltyTByBnhTHr61sPO1ZuZcymHtjBW9G7nWnGGPrCXJvenbuuaXcay3LvYLjl6rxLKto83Yq7fS80ysK6++FKIoB1sdIQa2KKEUrqsCRVQEQURVUhFlBVi2/vWti/E6rjipQVdbJhzXeaQMhg0SYd4nKiApVUVAd5bdwbYwiEtVRFSGF3+YRTUE8rEjXWvblnYxx1ER5vJryvipQEWYtuytFIlizz1irpIVUbXlfBaiMqAhJ26NACENALcaqKZwpBLEq8veQUsKZkMfVFIlTpXOtqpTODfsyVk3l3TmikVKrqUBUY/whVUFVhM/Nxb5R9q0sjomKqEbGmusT5+wxqZV9a6IKNIXxRFQeLyaNQT1fQUQFZ1UK776KQgqtIs+rWhZrLERH4LBaGpNKibN4jmSsVZFgTIK+zIOIxvhDKu/i6oxY1WLuhWXuRTWei4CfUD6e5Thn515C5h4AJHwFIY1jrapH5x5jVfgMr2n8p576ffr0vehVlT/l9kQipEAFikkc0ejGGoKAr5FsQd82DiTAEwwA8RBPIrnlHOzAkTUiPy8gmARkiLjsG5PTYx6PNtVhlVPJiKaQ+q8pRethHo/fRCXSCoqPBL6gRl5EK1lBKzNiZTLFQijiZCktcYYUpSxWBYqiFKeLQd/g3IRlvKrCLzZV5YKnoqDUJ6wUp7czcGolD7zgHMVm9Y0VYy2Rc4Ljqgp154LHiwBn8byG1GKsqlrC6QshX1OKsca0cnxKMdbSePKczoyV6ROc18QMnCgbTx6DsTLumHb0OQpyT1VmxipUFONXMXMsTi735HiiLPfKPkNTQCWpcLh0XZxiO32n96bJLbuBAQBAR8qB47OYRndZwJG1fKQMH9O6j7zN6ZLlCgxkXfgAuuR0qT/jwvYFRnKcngXT84wlMFHwOGXLu3A8gf4Mp2XdKRe+AAaynEqP5T3kbdJXk6aPrM0psOEIDGVZdNOT4vF60i48HxjKcco3XvCQsznNThoecnI6a7nAYJbH6ZZ9+aggiNNhfFnLR8r0MaX7yDsSp5zG+0KgO8Xpb/CIMpr3ULB9TOrsl7E4jdUdngPXE+hNu0WcnsRpuQJjBcY3rXtIGX5x+my4xOnJ6XwQq+tTadc8KlavOJ213CDWEs6+DNVpRnIudJv04LTlIx3EavNxwfEE+rPExzHhZ9muwEiOOKd0X47nzDFx/KNxDmVdmG75eHJMsjZxmq7AYJbj1zMLZ3nuZcrHJMApY/VRwhnk3rDMvUmdj3dp+Qily9yz/Vm5B5l7ruCidi7H6+FdO70PihE8D7jySgDAR1bEEQsJXLKQi2Ln1odREVbgyi2eirCKCxWgIsIFF00pLVZdtSSCeEjBRQsiUhKa364AUC8Xcy6ez/e8bwn7fHB5FJqq4IrFUVRGFFwwL4zauMrpqsJv68qIipqYissWkT55zTL2/cCyKCIaF2+qoyrOb4igKsrpKQS/9aNaGFURBZcviiKkKrhWLuK8fykXBS9ZEEFdjDjjYWkZ7VE19cL5nJ5euSQKVeJUFAVXLYkiEVZw4fwwGuJUrAnLu1ZdjLFevCCCWEjB+5eWcIZUxlEZIT23NkoKr6LQnbciTB26yxZFENFKOK9ZFkVU48JhdUwllTiiFC2842EFYS2MyqiCyxfzfAaLVe9fQk28S+SC2jkqF1eF4AJXVZQLoPGwgqsWk1p73QrivXIJF8cunB9GfZwKQyGVd8WaKBcdL10YQUwr4bx2eRRhVcF7F0VRHVHxnnmkHwdT6qimIBHiAuZ7F3Fx9QMS59VLo4iGSH+ujZXlnk+RlYowHwGPl3sXzz869xoSJOlcPD+CRFnuXbeCn3HF4igf/849F5g/n9P8d+1Cnm2zCME0gZdeAgDc38ICmA29RpGOGNBqA+rq1kETGdPHS13cNnlMbrk832UgJ6moozkX+0epftqRpHLraN7DpgHSUp/vJL3xsRZu2b3UpSNt+Ng2ZGEo6+HQuF2krO4ZtjBZ8LCh14DhcGsJAJ5s02G5pGZO6R52DZvoTbtonnRweMKmUu2QhaTBbSDHE3iilX2f7dChOwKv9ZkYK3jYO2qhK+mgfcrBgXEbQzlug2Usqt76QuDRlgJ8wW23rEVK5nDOReOYjfZpbi/ukzTUjf0m8g63gwBuR5HaayBp+tgxaGEgS/po86SNXqkAPKVTQdZwS9uaT7XrMFwf63sNTBVI2+1NuWiZoqrtYMbD9kELKcPHK906HF8UtzWf7dSRdwQ29lNReN+IxDlNheORHH3fcha32YTE6QmBF7t0ZE3SdYdzLg6O2WibstGdcrBX0ooD6u4zEucTraTWvtrDLbudQxb6Mi6aJrjF2Jd2sXPYxLTuY10vqdFPSpzPtOtz5940c28w62LboIV0We49GuRep8y9gblzb0zmXu4YuTdtesCePZzxZrNvypbd6VmcE+jemyaNLFesQHv/MLLCQcGm26jh+girSlF+KiwpoIkwNcYrI/y5ZuVSdPYPozJCrfNESIHl8RkboHxUVAN0l9/Ys/sEn6U71IN3fH5TqgrVaeMhtRjTUccLYi3Tgxfg86ftCsSPF2tRJ53vD1STwtrJ4YyHpB68fH50A5xSn/14OKNS916B1L0/WZyuj4iqFCWkQiqksszJjclsnMbJjkmZ7r3jk957IpyG4yMSohQYwHwIxuT14nwrc+/8qjgWex7v9AG19u3WvVcU5Qvy3/fLXvu0oigfVxTli2/oQw2D32yGAdxyCwDgnzeyDHftgRz6My6eatPROEon11e66Qp7/xHSG2/aw1LIr8syyh/tyiBt+rjnUB5dKRcvdOnYNWRhz7CF5zt1dKdc3HWIZbg/lJTIr29hKeQte7KYKHh4sKmAlkkHr3Yb2DJAl9Qn23QMyJJP3fHxne083n9uYxnuz/fnMCzLUw+N29jYZ+C1XgNNEw4ebilgLO/ip/tYhvtNWdr6vR0sw/3VwRz6Mi6ebi9g36iF7YMmXurW0THt4N7DeUwbHm7czTLcr0tPuxt3sQz33sN5dCapj79j0MTeEQvPdBTQm3Zxx0GW4QYln9/YwjLcW/dmMZ738HBzAc0T1IDf3G/i4LiNx1t1lhs3sgz3P2Vp67e3sQz3F405DGZdPNGq48AYNfbX9xhomaQX33jBwy17WYYbjMkPdrIM986DefRIJ9490u32hS4dnUkX9xxmGe6PdrEM9+tb0vCEwE92swz3viMsw325W8e2QZZGP92uoy/j4pfS/fd7Euc3t7IM92f7shiVpdFNEzY29BrY2Gfg8LiNR1sLGMm5+Nl+luEGOL+7PX1U7u2Xufdqt4HWKQcPNBUweZzcuzvIvU7m3m6Ze11B7plH597Ne7L0snv6aaC1lR71b3cZrqIoHwfQI4ToURTlMQC3A0gCWC2EeFxRlC8A2CeEaAz6nPGyO336non19Ov7TvCyWy3/rQXQI///CQDr5N97AHwcQOOcvY/Vyqm1//ZvwM034y8eaMG/XVeDn+3N4g8vqMCWAQvnNoSQs0hvPLchjM39Jv7wAnqffe26WvzjuiQe+3N6y33xmlrcfTiHT52dwMFxC4sqKB89nHNxxeIonu+k99n3tqdx92eBP7i7aQbl9Im2Aj64PIbulINEmIt/bdM2Prwyjoea8/i7q6rxtc1pPPA54I/vbcJ3PlKPG3dl8GeX0DftkgUlau2yag17R2z8t3PjWHsgh3/9QC2+uCGJRz5Pb7mvXleL2xtz+B/nJbBjyMLqOlJrU4aPC+aHsaHXxB9fVIGbdmfxjetr8Q+vJvHI5wX++uFW/PP7q3FfUx6/cVYcRyYdzIvT8KI/4+L9S6N4ul3HF95bhf/clsa9fwr84d1NRcrp31xejac7Amqth4gGNMQ1NE3a+PhZcdx/JI9/eH81vroxhQf/DPjsfc341vW1uHlPFp+9uBIbekmtTRolau2OIRP//fwK/GJ/Fl/5YC3+37okHv1zest95dpa/OpgDv9tTQJ7RiysqCG1drLg45KFEbzSreNzl1TiRzszuOOPBf7wnmb85Dfq8Y0tafz9VdV4qKWAj6yMoW3aQW2U1NrulItrl0fxeKuOv72CFOL7/hT4zD1N+MHH6vGDHRn81WWVeKHLwBWLIxjJeVAUylsfHLfxm2fHcfehPP7f1TX48sYkHvoz4E/va8bXr6/Fz/Zm8ZkLK7G53yzlnuNjTV0YWwZN/MF7KvDT4+Teb52dQOOYhcWVlPQekbn3QqeOv7i0Ct/bMTP3vrU1jf+8dh6WPf/ETGrtihWndNG+ac/0iqKsA/AlAH8D4HYhRKOcCXxCCPGl4H2vy58+n6dW3qJF6BsawaRLs4WIRpkjTSn5mYdUkifCmlJ8j+0JrFy2BP1DI8XfIxqJL5LzAE9wr/ZEfRyP6rCe4LOj8gb6BtLHqsJn7JOJdS6c5X1OhPO/OtaQIj3fxZuLc64+byfON5p7Qd+Tzb3ViRgWKwrL0qurTx9qraIolwNYVz6NP6VmmmTXOQ5w220AgH/bOkVvskN8fgz8z3cOWdjQS8rpIy0FTOsefr6fz1Xflc/Yt0j/7webSG98pdvA3hEL+0ZsvNxloDft4P4jfKa/RUpBfW87n6t+sT9b9Jxrn6Z/3Y5BC4fGKSM1lHVxl/Q6+7GUgvrhzgxMV+BXB3MYzbl4ul3HkQkHWwcpI9UyRXml8YKHtY30WPv+DsZ60+5M0WuuP+PixU4+J+8etor+aw83F5AyPPxsXxa+IE5fCPxU+rk/1EwK8boeA3uGLewftfFiJymn9x6mXNZNuxnr93bwmf72xhwmCh4ebyvQp6/fxLZBE4cnSHsdzrm48yCf6X8knz1/tCsDw/Fx58EchnMunm3Xi150r/WZaJN+7JMFD79o5DP99+SY3Lwni5z0b+tNO3i5y8D+URt7Ryy80m2gO+XgwaY80qaPW/dmISROTwj8fF8W04aHR1ro776+18CuIQsHxmy80Ml1lnsOUy7rRonz+zv4TL/2QA7jeQ9PthfQImXBtgyYaJp08HS7jtG8i18doFxWIHl1467MMXMv8O87Ue490JRHT1nu7R2x8Uq3gZ6UgweaZubed2Xu3bY/i/GCCzz/PMvRp6f57xTbCe/08rl8dusRQqwve88XhRA/kP//PvgFsF5RlE+Dz/c/CN77yU9+UqyUyh833HADbrjhhqM/PRDQsCxO89/zHuxpH4ASZUFDQ5yOnrGwAt/nN2Y8RO3xhriK8YKHRZUhjOZcXH7ucjR2DmJxZQiTOimgui0QpngJbI9lpCnDx/wKDaN5F5evWY7GjkEsrgphLO9iYYWGpEE3UtPlN7WmKjAc6tlPGT4WVmil48m+43kP8ypU0nLDKmwpjBkJKcjb1DyfLPhYWKkdFWsRp3SR9QXvRIkT4FxUoWHK8Is4Qxq/2U2PPnhJw8eCOXCO5z3Mr1CRMnxURlXYLu+eIVWB7vioiamY0o+Bs+BhXkJF1vQRD5ME5ct6hJzloy6uYuJYY1LwUCd19qMa756OR/nstOljXlzFWMGbc0ymDR81URW6y7u2qnAVvTqiYjrAOceYzK9QkTK5ym57zP+IqqDg8LwdNSay77FyLxZSin4Bx8y9gofa+NG5VxFRkD5O7l1Rn8CSQoFedrW1vNNXVJz4wj6VO70QYu0c/8ov+C+UXfAfB/AI+GwP+XN9+eetXLkSa9euxdq1a+e+4AHu0yeTZNlt2AAAeLwjD8Pl3uyU7uPAuI3+NGWlmydtjOS5T5y1uMft+QLPdXKfdV2PibzNvdnxPPegu1MuelKku44XPOwYIuV0nZQ9fq6T+62v9ZlIWz52j1gYyblonrTRkXTQn+E++JSkaZquwEtS9vgFSc3cPGAgZfjYP2pjIOtK6qiDoayLfSPc193YTwnq57ukVHM3KaHbB01M6JTK7ku76Eo6aJqwMZr3sGvYQs4WWN9LCexnO0k93dDLWoNdQ9z/PTJpoztJ+exD4zYmCx62D5koOD5e6Q5w8vivSbru3lELw1nutbdPU367ccxGUvexZcAkZVj2famb+9lbB0wkdR+Nkk7bMU2K7HDOxZ4RSmBv7KcEdjAmr/YYKNg+tkt68qFxCz1pykofnqCk+a4hSmCv76UE9rOdOjzB37M2ZcJH8h6aJ210TnOv/eCYjUndw7ZBE4bjF2XQn+9iPcTGfgMp08e+EQtDWRdtU6yBGMy62D9qI2n42DxgFGm4Ac5i7hlH595onnv35bn3bDH3DORt0o4n5si9iTxzL1+We8+W5V7K9OnnOD7OG2Eud6JL9oTtlBby5EX+fUVRvgSgHsAfyGf5K+Xf0m9oyh8KcU/S94FLLgEAXLOE1MgL5oVRHVWwujaE6qgKx2elWnWUFWGJME0KNJUVagBw2UJWoZ3XEEZdTIWoDRVrwatlBdf58/ieSxcGlVSsILt4QQQVYRo9BBVVrPEGIhoNDN4zL4yIBly+iGYFVyymOcKF80m3PLsuhLq4Kr3aWOGGelJmL14QQUgBrlzMvu+V1X3ny4qx1XWscvN8yjvXxtSiMcWlC2n+8L4lrMi7ZEEEsXAJJxAqkpKC6sH3NIQRk9WCxMnjXzw/goqIinPqwmhIaMUa9WhIQVijIcWF88IIl+G8fFEEYQ24YF4YVVEVq+tCqI1ykdMVnFmsqSfei+fTbKI0JqS+nt9Aw4pVtWGagQgSTupkhV88TOMIRVFwlax2u3QhK9jObQijPq5CU0LFWvp4SEFNlBV3kZBSjPXKxRGEVBqRVEZUnFMfxrw4HYyhyBp5Sci5cD5NPK5YXMJZnntn1YZQMyv31tTPzL2guu7SAOc8VvOtrAkV+Q7Hyr33leVeZUQFVq/mXT4ef/sr8oQQ64UQdUKIs+XP9fL1tfJvJ1ixO0bzfd7thaBPPYDBHOuhJwoeTI+WTgWHNkFpy4fuCkzpHmyfddW+YP01AIzmWTs9pbOGPGWwVj9ns37adFj77fjAWJ4100NZfsZ4wYPjsUbbcATSFuvu8w5jsFzaEHk+hQ4BYCRHG6SJAuuxk4YP3aZFVcbyoTvkC9heECvruoO+jJWWTUmDNeI520dGxjqle3BlXyFxCsG6edejZZXh0kopiDUlV9QnddovjcpYh7K0UBoveLA9cgt0h3XsWUugYEucHs+FJxgjQLyeoIUTY+WYZGWsuuNj2uDnsu/RYzKp+zBdgbRJfkLOZl26IcfT8QVG5ZgM5yTOPF+f0uWYmOxXsGmTFeD0/FKswzme5/GCB1vGOgOnQ7qr5ZFDUI5zNO/Bl7lnuUBqjtybNubOvbHZuWfOyj1XFHd15so9yxOc9VoW17jetbZWQROiyCoKKLSqokAB68mB0kp66W8orsyXfioz31v8qUBVBDDrMzD7MxRAlW9SZ7y39DlH9ZnxdxRpmMHBghiKnz9Hn+D12a8pcx1HUYqfFcRXfi6U8nMj3zNXrOX4grhnf9ac51eZoy+UGWOiHLePImMUcxzvxOe3fHyPhU/+qfR3pey8zHEO5sI5M39mxX+sc1N2LstzJsi9Y+EMzgNUlTfCAOgpttPzoldV0gkBKoYAWFxB++f6ODnbtVLyOKIqiGjUZgu85uYluAe/SEoNz0+QJ10XUxENkXceTOsAFTGNyjKaCsxL8EtmUSU/o0FO6Wtj5GwHfOywxmkk97LJ716Q4PEWVJD7Xx+n1XKt9ExTwO2seEhFbYxbPPMSGlRwnzjoqylAvfSTC2J1NQVhjSWmdTHaTc9LkGc+E6cyA2e0aFWtIBLi30IKj1PECe7Hh4qxqvAiKNJ3a2LkgjfEGVvQd0GCvzfEeR6qoyppqCo58TFpIx3SeB4VebxirEownuSSUzmHF0M0iFVVMF+OycIK7m/Pk9bOtTE+hlRHyckPqYArzxun/aVYF8oxmZegzXWA0xc+Kbcy1rBGe3C1rO/8hFbMvYjMvXhYKVKkY2WxBrm3sGKO3CsbT5noiGpB36Nzb560JEd1dYlTHzr1S/b0JNy4LvfoLQtoaQEA7B0zYXsCHdMOsrZAX9rFlO5jrOBiWCq29EhVlJYpSmUfGCMNsWnSkYo6blHNZVyq2ASKOF1JUkubJ0lvPDBmU9FmyobuUOEmLVVkRvNUsgnUUNql2s3hCR7v0LhdVJjJS2WdaYMqOCM5Ujl70y5020frlA1XAAfH2ffIBGsROpJOUSVnQvcwnvcwmHWRtnx0JR0YMlZf4hRCEKdDCmrGJM6JgodJ3UN/xkXW8tGZdGB5AkcmynAKoHXahm7zHCZND8M5D6N5qsP0palu0z5NenOA8/CEDcejwkxeKt1MGz7G8uyfMjypHuTLMcHMMZGqOIHyzGTBw3jBK6r3dKVILW2apDLQgXGOa/Mkx7k75SAlVYjGynDmLJ4/2xPFWA/KMWmbohpNb9otKgqNStWeXqlW1CZxHhqfiXN27o0XvGLudaccGI7MPV8Ux3Ou3JuQaj0nk3sFx2dJejDFN81TvrxOzzt9JALU1/MZ5vrrAQC/t6YSWsjHNcuiaIiTOhkPKfCEBs+n0EEiFEV1RMH1K2LQFAWfOofEhI+uiqEiTJplXTBDkBUSS6pIV33f0igqIio+IjXcPnVOHJrKz6qOkuYYLLxQXAJoSKiojar4wDIu1nxiNY/3ydVxRDTSZeviKt67kItkCz2q4Qbf+DUxFdctp0bdb57Nvh87K454mJpyDQm1qGLjC8DxKQbxviVRVEUUfHglNfI+dU4ciqLgIyupHXfVEuKsjKgISy2SRRUaKqMqrl4aQyKs4mNnSZxnxxFSFXxoeQw1MRWXLyb1tD4uoAIIaZx11MZUXLucVNrfOIuxfmJ1HNEQNezqJZ01EVbg+lpxy64iwoW961dQI2/mmFCPrj7OWVRUUmsdn9Th9y2JojJMXT1FUfBbZ1Mj78MrY6iOcGGvJsbP11QU7+zVURUfWBpDPKzi4zLW31wdR1hT8MEV7PPeRVxknZfg40RYo75ebVzFB5eTGv3Js0s4Y5I6Pe9YuReOoiqq4MMrqG/3Kdn3IzL33idxnlTunV3KvdqoClx8MbBkCbfq3rWutZbFLQrDAB5/HADw84MskHi+08Bo3sOWARZ/HBq3sXvEQl/axbpe0kMfb6Oa6J0Hub3xcEsBWUvgpW4SR3YOWWiaoGvojkFu3bzUpSNr+XhEqrXeeTAH1xd4vE1H0uB2Sp+k0x4at9E+5WCLpIU+28FttvuPUAH1niN5mC7VaSfypLN2Jh16tY1a6Eo52NBnYEqnAqrtCdx9iH0fbCogb/t4vkvHSM7DtkELLVOk5O4eNtGfoe9b2vTxaCsptXcezBUptmmLdN2BrFv03GudcrBtkMqrL3TpyNk+HmoizrsO5UntbdcxrZM+2pN2sG/EwoFxG53TLjYNmBiX/m+G6+M+ifO+I3kYjo9nO3SMFTxs7jfRMc1ts30jFnpSDjb0ksr6RBuptXcdZN+HmgvIWT5e7NIxnHWxfchCy6SDpkl64Q1kXbzcrSNjUZVWCIE7DuXgCdJzUyZx9mdI/Q1wbh0wMZr38FynjoL0BASAuw/TM/Cpdh1TBR8b+0x0pRz6yo2R1vtav4nJgodn2kmNvucw+z5wJH/M3NszYqE3TY+6lOHjsSD3DjH3HmmWudelYzDjYsegheYJKumW516mPPcOMfceayOJB1u3sl4lkwHS6VO+vE5faq1hUBxzagpYvBi9g8OY8iiIGA2x7FFTUaTWhhTA9nkXDd5juQKrli9B3+BI8fegb6A65MvSyxP1sTyBiAq4gt+UioKiDtyJ+tqzSj41hXezk+lbjPX14PTopOr4vFtDef04vVnlqa8Hp5AUYu2NjoksTw1wvJ4x8U4Sp+0JhN8EnG917p1dEcNiAGhoKN3pT4cy3De9GQbQ28uf3ydj93+um0DBoQtpX5rU1D0jFjb2m3i+U0fLlIM7D+YwpXv47o40PF/gS6/R4fNb29JImz5ub8yiY5rlltsGWE77RBudT29rzCJj+fjGVjqTfOm1JFxf4Hs70pgoeLjrYA5Nkw5e7NTxWp+JvSM2Hm5mqezNezLQHR9fla4mX9mYhOkK3Lg7g+Gsi/uP5HFgzMa6HgMvdxs4NG7jnsN5jOVd/HBnBrYn8K8y1v/YkkLO9vHTfVn0pFjGunvYwuYBuvG0TTv41YEcpg0P35blt1/ckIQvSAVNGXRObZuy8Uy7ji0DJnYNWXistYDulIOf7Wf5639sKeF0PIEf7ExjPO/hnkN5HJ6ga8yGXpbGPtiUx2DWxU92Z2C4Pv5N4vzqphQMx8dNezIYzLp4qDmP/aM2NvSZeLHLwJEJB/ccymG84OH7O9JwysbkG1tTyFo+fr4/iy7p+rpzyMK2ARNPt+ton3ZweyPLir+1LQ0hcXpC4Dvb05jWPdxxIIeWKbrGbOo3sXvYwiMtBfSmHdy6j+6/X9vMWL+8MQnbo2vuaI7lyAfHWQq7rofOwPcfyWM45+LHuzOwXIGvbGSs/745Vcy9/gxpuXtl7r3QqaN50sFdB3OYLMu9L25g329uTSFt+viFzL2n2gvYPmhhx6CFJ9vLcs8s5d4XNzD3vrsjTWrto4/So35yktJZp9hO3zs9cIZa+xb3PRPr6df3nUCtfWtacKevrQW+9jXgxhvxhYda8cVrq3H7/hx+/z0V2DZo4py6MPI2ix3OqQ9j2yAdUm/bn8VXrq3Fv2wgNfKvH27BP72/BvdLyunhCVtu/wCjOQ+XLaJD6p9dQifYX/4R6bE/+Fg9vrc9gy9cXoWn23V8YFkUvWkX8bCC6oiKDumQ+lhrAf9L0jjv+Szwufub8c3r63DLngw+e1El1vUauHhBhEU1klq7f5QOqXcdyuOfr67BVzam8MDngL98sBn/em0t7jiQw++el8CuYQurakitTVs+zm+gO+8fXkAa579fR8fbBz4n8LePthYppx9bFUfzpI2GOLehBjIurloiKcSXVuH7OzO4449Jj/3uR+rww50Z/NVldHN935IoBrMut69iKlqmbHxkVRwPNxfwf66qwtc3k5b7+Qea8R/X1eJn+3L4zIUV2NRv4vyGMNImi1xW1oSwe9jCDecm8KsDOXzxAzX41w1JPPhndNj94jU1uPtQDr+9JoF9oxaWVZFaO2X4uGh+BOt7DfyJpBDf/hmBP7mvGT/8eD2+vTWN/13mJNyRdFAjtwt7UnTnfbpdx1+/l06wd/0JcX7nI3W4cVcGn7+kEi91G7h8UQSj+RK19tC4jU+slhTi99Xg3zencN+fAn/+gKQ7z5F7BUfg7LoQtg+WUYjnyr0jeXzy7DgOjttYJLfzxvJluXdxJX68++jc+49rGrDspaeB664jtTYWA5YvP6XL6/S90+s6JbMmJ4Fly9DZP4y04PZPIqzCkiQLHwG9kWWq8RCliSrC/HnOiqXoGhhGRZgSSbGQAtvHDHpjRModxefoE3yW4frUrpc1Eir4XB4LKcWYZvcNXjddkiz8MmmmE8U6F05/jlhPBqcCKZd1nFjnxAmWTDje68QpTn5MdCntZZfJZZ30mEhpL8eXRUyvE2dEU4pj8rpx/hfl3nmVcSz2fe5mBdTat1su6y1ppklXD8cB7rkHAPDdPUkUHB+PtBQwlHXxao+BpkmuEm8dMNGdcvFMu45pg8+lnpS6AoA7DuaQsbiC3JdxsbHPwIExihq+1ssV4Mfb9KKLKgDcuicL1+cK7rTu4dkOSjhtHaD8VPOkg1e6STl9uLkA3fHxi/3s+/N9OZiuwANNBYzmuTrbNkWfte1DpGK+0GkU3XBtT+CnexnrWum2+mgLHXHX9xo4PGGjcdTCln564j3VriNlerjrED3sbtlDiu1dB0lFfapdR0+awpL7R4lzfa+BgQylu3LSFRcAbt2bheMJ3Hc4j8mCh+c7DXRM079u9whX1F/u1jGac/FgUwGGS5daALhtP6m2DzVTZuqVbh0tkw72DFPeqzPp4vkOioPedzgPx6drLAD88gBlux5v1TGQpW/dwXEbB8ZsbOoz0Jt28WS7jozp446DOQiJ0xPc6UgaHp7u0NGTcrGln1JZRybotjuYdfFoSwEF28ftEudP91KW7IEjeYwXPLzYRZw7hkzsGrbQNuXgpS4d43k691oupbUA4HbpSvxwM9171/UYaJp0ZuTesx3HyL0Dc+fewbFj594tZbk3obvAunWc+aZS/HeK7fS805smn+dtG2hrAy69FFtb+xGLCwxnXSyopGNpIkwiiudTlDBlelhQoWE452F5dQj9GRdXn78cu9sGsbxaw1jeQ0NCQ86iKKICCjdWRVVM6R4WV2oYzHp4//nLsattECtrQhjMulhSpZEaGdNgOD5UWf2l2wK1cRUTeQ9Ly44X9B3KulhUKWm5Ed7NfAhJxRSYl1AxMivWoO9wzsWChIaM5Zft01PsMWl4WHgMnMuqNYznPdQnNORtCjgqCu8mNVEVE7qHJZUaBrLejOMFOKcKPqpjdLxVQQnsvC1QH1cxlvewbK5Ysy4WVmpIGXT2dXwpgR0irXhexdw4V1RrGM17mC9xxkJ0ALI97l8ndQ8LKzUMzTEmS6s0jBc81Mc0FBy/KIGtuyQlTRQ8LK06OtbBrIsllaQfV0cVWG5gPAHkbIGGuIrR4+A8Xu7Nr9COwnms3AMoxHmi3HtfQwLLcllg8WIqSUWjJKOdoL3z7vSOw/1IzwN27wYAvNqnw3QFGsdspA0frVMORnKswOpKscrp8AQrw3YNW/CEwMY+UhV3DJnQHVZJTeseOpKktw5mXbQnHUwbHg6O29BdgR1DrHja2GfA80nfzFusYJsoeOhKuehPuxjJeWiZspE2fewfs4sUUwDY3M/qwX2jpJUG9MuetIOelIvxvIemCRtZy8feEQuOL7C5n7FuHzRhuD4OjNlImqwOG5I4O5MOpgoeDo/bKDgCO4dIrd3YR4noncMmCo7AoQkbU7qHzqSDgayL4ZyH9mkHScPHwTEbpiuwfZCxbuo34PoCe0Ys5CyBI5M2Jgo+elIu+jIORvPEmTF97B+1YHkCWyTOrQMmLIkzbbLqbjTvoS/tojvJqscjkzbylsCeYQueP3NMDJfVhNMG4xvKukVq7pQux8ThmAiJ0xekDhdsgcPjNiZ0D51JF/0Z4mybcpAyfDSO2jBcH9sGgzEhhXjfiIWsHJOxPCsGe9IOxgqk6GYs0osdj5LpALBt0Dxh7h15nbk3FOSefvzcy9o+b3zJJB93df2UL6/TcyFP01hr7PukFQK4sIF0xxU1ISQiChZXaqiNqXA8AccHqiMqlldriIZIu9UU0lMB4Jw60iyXV4dQGVGxqFJDQloIRTX6jK2oJj3z7Dr2OX9eGKoCrJY03GXVrPQKJKxpWBBCIqxgZU0IIQ1YU8++5zWEEFKBVTUhJEIKllSFUBNjdZ0AUBlWsLRKQzyk4qzaEEIKcF4D+66pDyOs8jMrw8RZHSFVtdJVUBlVsaw6hKiMVZU4FUXBOXWkzS6vDqEqomJhhVa0UwqpFGxYURNCWFPKYg1DK8dZpdHoAlrRysqrJB10ZQ1xnVtfijWkAqtqeR6WVJFyGgsJeD5QFSXOWIh0VFXBzDHRGE8wJpURFULQN74qomJFDXGeU0d85zUQ7+q6EKJyPKsjKrwK7ueHVJKOKmSsEVXBmrqZOFfVhhALK1gqY6VlGKvqllQR56qaEDSV4wgAa+rCx829qoiKZdXEubo2BBWl8Tx7Vu4trNBIrT5O7hEncFZtiBZXixaVHGsDTsoptNPzoheC9feaxhp8ABnLhw8uprg+p6u2F/wDnLCA7gj4PoUyhSCVFQBytg/fp+a76wsYjoCmUBnGcPlawaHaS97myk7WYsls3hHwBD/b8QVMVyCicUpoOEzuguPP6JuzBYQACo6AKwDT9eF4LCbxBQtADJefm7cFfHm8IFb2JU7DEYhpwecIuJ7EKY83G6cnMCNWVVGgKcTslsWaC2INcNrlOLkwpSpc4DLcACdxBX3zMta8zb/rjkBlWMByeax4SOE5Ejy/Qh4v6OsLzBjPiEZcZjAmtsTplJ9Xjm8QqytxAlxANNy5cWbLcDIXfDg+F0oVWVZtOD48X4Mucc7IH7CPJ2N1PAFL5l5iVu4FsRZxynMXxBpSj597OTuIleMJ0+Ss1/dLq8Gn0E7fiz4AJ6czOSdIEgFPnjzXp+SQJU+e4YriewSAgjyJvEgEDJcJZnkCUVkeZ3tCJp0PXyYSZF8BDrRfdsFRXol3FMtjLIZMkmDQCsUkYYKZLi8kW170weAHyYeyxA4S3XAEXCETyxcybhQvEG92rEIUcZbODRMsWF0OYvUFjwOULlzdYXKaHs+l5bLiMaIp8nhMUiFK5zXoa7oy1jKcrs81CEP21R2/mMgAiokeJL7lCjghvhZ8aRhyTGbEWnZeDZdfbpYX0FHlF46QuSDfC/D8Cnk8r2w8gy+3qKbA9ETxS9MHvziCWMWs3HNk7tle6WL2ynIvPyv3zGPlnjh27gWxFn0d39UXvaZxW8L3uTcJ4D31ZdP7MKeDVREVFWEOfFVExdIqDZGQglW1IaiKgnPkNPSsWk6fllWHUBFRsKBCKzmvagoqw/xbROM0FADOqQ9DUzjVi4YULKnSUBWlXUxIJaVXVWgHvbya097geGfXhRFSGGssrGBRJVV+ohoJJQk5bY+FFKyqDUMrm4aurgshrAHLqjllXlihoSLCraXKsEClnDJHNeJUJE5FYexRjbFWRhTMT2hFp9WwqiARIc6wxuMAnKJr8nEiFlKwpJI4NcnPj0gSTDysYMUsnOfI6f3y6hASIY5JTVSVZBQuOi6R0/uVNXzkCh4rVtdKnFUhVEiciTCtqhNhWj8HY1Ieq6oQdzTE81AVUSEEy1k1ldqFFXJMwmoZzrowQuU4qzgmIa3kZrtYcDq9ooaPXOfUBeNJ3LNzLxHmBV8lcUbLcm/N68099ejcW1kTQlyT0/vqak7t34Tp/em7kJfJcL9+zx4AwPp+kiAaxyykTC7YjOS4gNNdtphSsAX2jnDRKFhw2jVsQXcFDo3bmDZILx3Mkv7ZkXQwbfg4OG7DcLgQAwBbBqh1tmfERt7y0SQX8nqChby8i9Yp0m0bx7jAFSyObRs0YfvA/lELWZP02TG5wNWTdjBe8NA86ZQW8jyBLbLvziELpsuFn5Tho32ai0YDWS4aTek+jkxwIW/3sAVfEKcv+HvBETgyYWNK9+dcyDs0bsN0BHYOlXA6vsC+URtZ20fzpMSZdtCXcTGW99AaLOSNWbA9FBcstw2asDygccxC2iLO0byLvgx1+SYkzpzlY++oDdenpxsA7By2YDock6Thc4ErR1ptZ9LBlO7jsMS5a9iCEOzrBTht4pzUubg6kOHiavu0g5ThFRcsdwQ4B004ctGxuJBX8NCbdtCbJs4WuZC3f9SC7aO4CLh90Doq90bzPGZPysWk7qFpgjTqIPc2nyD3hrLMvSk5Jrp7dO7tHZELee3tJKDp+puykHf6btnl89yy6+sD1qzBga5BuCEP0wYVbfM2t758n1OgaChQmNUwpXuYl9AwqXu45OxlONw9hPkJDUnDo3qqQwELAHA8LhxlLB/18aP7TOlUQE1bUj3VDZ51Oe2tiihImT4a5ug7rVPpNWfRwdX1OfWj8qpATVTBtOHPGWuAs2BzkcpH6TmZCrPsM3+OvinDQ1VUhSELe1RwPaEioiBjHh9nxhKoCJNUEqjhGo5AVZSKwQ1zxRrglGPi+ZwOR0IKCvbxcZaPSeQ4OMv7BLhTpoeqSEmhWFVKONPHGZP6cpxyqh2WOKujCpLHwnmC3KuNqieF8/Xk3qW1cSwxTW7ZVVayIi+ROOF19s7bsguKcwyjWJzzvd0kPTzaUsBwlg6qTRM29o7aLJBIOiyQ0D3cc3hmgcSdB3PImD6elAUSm/pNHBizcGjcwmt9LJB4so30xjsOlIpWXF/g3sN5TBk+nusw0JWkdv2eEQvNshBkOOfhkWJxDo/3831ZmK7Ag80FjOU9vNSto3XKxq5hEi3apx280KVjouDj/qaZxTm/lMU5j7cWMJSlI+7hCRv7R20W56RcPNOhIykLQWYU5xzKIWV4eKpdR68szmmUxTkb+lic83grKa2/PDCzOOf+I3lM6D6e79TRkXSwXfqttUzaeLlHx2jOw0MtQXEOY71tfxaG4+PhlgJGcx5e7TbQMkm66bZBE53TDp7v1DGlk47r+PTMA4BfHcghWyzOcWcV55jF4pyUSbJTeXHOPYfo5fdMO30ItwyY2Ddq48iEjXW9BoayHh5rIUV57azinPubguIckpd2DlnYNSSLc7p1jOU9PNCcP6o4J8i9kdzcufdch45pwz8q9+6YlXsbZe4dlLnXF+SeLEICSsU59x7OY1z3gPXrgc5OFuYkk6d8eZ2ed/pAIaRQINAFCzA4PIIxh4oimspnxuAbywegKUrpb2U/ly1dgqHhkZmvn6DvnH3kT1+eL1Xh57zhvm9SrP8lOE/2eG8hzuMd778cZ9nxxFuMc2U8hsWaxsKcYNvuXUut7e7mz299CwDw5y+Po+DQ2bNPOtLsGrawvtfEM+06miZs3NZIau3Xt5De+Pev8lvx3zaR3njL3izapx081lLA5gETWwctPNJMeuPNe0it/cpGljn+/aukN35jK6m1tzfmcGTCxjMdOtb1GNg9bOI+6ULz/Z2k1v6LpFP+83pSa7+7ndTauw7lsW/EwsvdBl7oNHBgzMKvDuYwlnfxrW10XvnHdez7r6+lkLd9/Hh3Bj0pBw82FbBDOqk82cYZw8/20+Hla5tT8AVx+kLg3zenkDI8/HRfFq1TNp5s1bGx38T2IQsPNZFae+NuUmv/9TXi/IdXSa391jZSa395IIdD4xae69CLbiz3HCa19ns7SK39f+sZ679sSMJw6IA7mKWrzJ5hC6/2GHhOusCsPUBq7Te3klr7D3JMvryR1Nqf7CG19pHmArYNWtjUb+Jx6SZ0615Sa7+6KQUhBP7+1Wl4QuA/tqSlm0wOzZM2nm7TsaHPxM5hCw8cIbX2R7voFPQlifMf15Fa++1taYzm6N57YMzCC50GXuoysH/Uwl2HSK39zvY0LFfgnyXOL25IFnOvP+POyL2nZe79opHU2lLuTc/IvZv3klr7WEsBW6SrzqMtZblnHp17X98iqbUPPAAcOcLn+jPU2hO3MzTO0+d4p9L3nRTrqfT99abW9vcT5Le+BXz/+/g/j7bhH66uwh0Hc/jdcyuwc8jE2XVhFBwfeZv0xh1DFn5X0jj/5Zoa/NumFO75LPC/H23F/7mqGg835/Gxs+JomrSxIEFq7Vjew6ULI3i1x8CfXFSJm/dkcNsfkjb6nx+uw493ZfCXl5Jy+v6lUfSl3WLFWGfKwbXLYniqvYC/fm8VvreD1Mi/eqgFX/1gLX6+P4vPXFCBjX0mLpwfxpTO/djFlSEcGLfwydVx3H+kgL97XzW+viWFu/4E+JtHWvD/rq7B3Yfz+O1z4tg3YmNFTQiWR3338xrC2DJg4n+cn8DtjTn86wdIy73rTwT+7vE2/K8rqvBYq47rV8bQNmVLRV5qqV+xOIIXu0jjvHF3Br/4DGmj37y+Dj/Zk8HnL67CS906rlgcxVDWRUQqtbZNO/jQihgeby3gb66owre3kZb7/z3Ugq9cW4PbD+Tw++dXYOuAifMktdb2BJZXh7Bv1MJvnZPA3Ydy+Mera/Dvckz+9pEW/IOkO//m6jgOjNlYUqXBE9SIv3B+BK/1GfjDCyrws305/PTTAp9/oAXf+WgdfrAjgy+8twpPteu4dnkUXUkX1VEF8ZCKvoyD9y2J4rlOA39xaSV+uDODtX9E99ivf6gOt+zN4rMXVWBdj4lLF0YwlnehKlTcbZp08NFVMTzcXMD/vrIa39yawp1/Qnrslz5Qc1Tu5W0fuiNwVm0IuySF+I6DOfzL1aXc+1+PtuD/XlVTyr0Ju6iyO17wcMkCUoj/+MJK3LI3g5+X5d6PdmXw1fc1YNmrzwEf/CCwciUv+HcttTaf58U/MgKcdRaae4egK1ROrYoo0F252itI7ohoCnSHe6YZk95rGdPH+WctRVvvMGpiKnIWCSGsiuIKqutzJbZgk/wwu0/wWTnbRyLE1V5V7mHbnkAipCBrk8xyVF/LR3WEcUVDJGgIAGFZ5VYZ4Xvm6jsDp8r9a98XiIRODmciosB2+ayogIUysZCCvE1HlrlirYmqyNsk+Dhl1Frb5SrzyeCMhFhT4INxnwzOSjkmYZVlyl6A82TGJEycqqpABWD7HJPcSeCMhUoUYk1lUVDFyY5Jee6pfO2tyL0La+JY7DiUgq+u5vP8u5ZaOz7OUtzHHgMA/PRAGroUYRzNe9jSb6JtysEh6ejalybdNmV4eKyV4oTBauhDzXlkLR8vdusYzHrYMWShacJG8yQdVoeyUjDS8vFgM8t+7wjECVsLmDY8rO8h3XPPsIWDYxY6ph1sLgpj6jAcH/cGwpiH6Xr6dHsBE7qP1/pmC2O62NBrYFL38ERrAY7HlXcAeKApj4LNVfSRnIdtAyZapxwcGefq/0DGxSvdFMZ8pIXCmHdIYcxHWvLImD5e7uZK/c5h0k1bprjKPJzz8HynjnyZYOSdh3IUxmwtYEr3sL7XQE/axd4RCkZ2TtPBdrzg4Zn2AkxX4J4jjPXeI/QXfKZdx3jBw6Z+Ex3TDg6M05W1R4qVTuseHm8twPEpbgkADzTnkbN9vNClY1gKgDZPcgV+x5CFwYyLl7q5o/JQc57CmAcpjPloawEpk7sF/WkXu4YtHB630TZNYcyRnBTGdHzcJ3HedYjuwE+20UV3Q6+B7pSL/aMW9gfCmH301XuqrQDLE7j7MGO970j+qNxrl7m3Z9hCXyYQxjy53GuenDv3Hgpy72Ap9yZ1D9iyhTLY6fSbIox5ek7vAwls1wU++lEAwO+vqUQ8JPDB5VHMS2i4bFEElWESUVzpPBvRKFP9kVWUIb7hXO5nfvysOCojCq5ZGsMCSUKJSXWJJZWkYl6zLIaKiIJPSMnkG9YkEFIVfGQVZYivWkIJ4xppFhGSqjINCQ0fXE4J7EDG+lPnJBANKfjQihjq4yquWBxBdVTFggoBCBorVIYpU/3hlTGENQW/vYaxfmJ1HImwgmuXxzCvQsOlagSJsAovwBmllHdVVMHHzqIE9u+sSUBVFHzsrDgqowquXhbFvISKijBJPqpUhqmLa7h2eQyJcEmu+3fWJBDWKCtdG1Nx1eIoauP0klMVluHWxlQ0xDVctyKGWEjBp85mrL95dhzxkIrrVkTRENdw+aIIKqMkoviy8jAeouT0R1ZS6vsGifM3zoqjIqzgA8tiWJDQEFlAcwwhOIOqjqq4eikr8z6xmhLfv7MmAU2hJHa1lI6eF1dpQKIBIWmEUR/XcO2yKBIhBZ+UOH97TQIRTcpKx1VcuSSK2qiKeXFWWcY0BVVRFXVxFdevjCGqKfitcxjrJ8+OIx5Sjs49n2W0leGjc+931szMvauXxooEqFgggV0pUFOWe4Fc9++U5V5dTAUuu4xVeVVVb7+X3VvWArML36cgIIDdoyZsaayQs2jAMKnTrGAo5yJp0gRCdwWaJmiKsH+UC4JHJlid1ZF0kDFpIDEmzS76MzSQ6Jim0u4RaY6wf9QqGSs4Al0pUjaHsi5G8h6mdA+9GRc520fblAPbLxlWHBhjlV3LpIO85aMnMLvIeRjK0VihO+2iYAu0TDlw/VKsh8dtWB7QNkXqbV+GOMfyrMpLy6ouwyFOXwjsH2PF2pEJVtt1TLNScDDrYizvFnFmTVb4WWUmEPtHWUHWPOmgIHEmDZp6jOQkznQZTk/goDSsODhGY462KQc5mzindJpHDGVd4kzx/DVPOvDKcU6Qjtwx7SAjcU5Is4uBjIu0SWqw6TJWIXH6grh1V6ArSbML4qSBRF/aRc4KcPJ8BjgdX6B1ilWbPSmOyXCOBiRTBunEedtHy6QDxxc4MMZYD43bc+degDPIvQCnjLU89zrLcm88wJml2UXHNHEWc2+slHsFx2eBWibDx913rdlFua3VggUAgKVVpDvOi7O+vjbGO1lYE4h6AvGQUnSVXVBBq6bFlSWrqJCqoEGaKtREVVRE+KwrBF+bJy2hgkWWxdLuaUGFKg0fNMTCNKkIq4q0I2K13Dxp77So2JcWXPMTWtFKilZGqhSX4GsRTVomKcCSKg7FwkpN2mtpiEkDhkSYxwurArEwcRRxKqyXV6SVEi2kaNlUHeWxNAXwBGvDG+IqQopSFisXNBdUqIiotOJKhBS4URWqQqON2tk4K0uWWJq0igrsmRJhFapCYko8rBQXEhdUcOYQjMnCWWNSG1OLrrWqoiIWUlEf55gEdlZLKmmNtaCC1lT1cdb5B/ZdYZWWU8VYVZ5PgOc3iDWioWh64gnmQSKkSNsqpTgmiypDxVhPlHsN0sJsfkKFCmDJSeReYKk2O/eWlOVeRFNKvvTh8LvY1ipo6psT3mzfvzfJB7D0eSd53FP5rLeznY4xHau9mbEGn/Vm58sbam/StQCcrhd9YFXtusVihGFpVT1l0Go4bfooOD5ylo+sRWvjpEEL44kC7ZcD6+jxvAfXpw2zKfvmbfKY09IueEr34fq0BwakPTGAiYIP1wOSpgfTEchatBnWXVoNWx6thj0BjBX7ukVrY9ulPbHusm/WEkXLYtujzbUvgJEcLYjH8rS9ntJpyZ22uC2Us2mrbDrEUcQpBEakZfW4tKqeNnwYLu2iA8XWtEk76WnDhytEWawehCBO2weShleMNSdttY/CmfdKscotNsuTOB0eM2v5MBw5Jh4/3xcli+zxwhxj4gjkHUFLbtdH0iiNiQhwgufV8Wk3bbi0/w5wBrFOSfvwINaRnAtf8Hw7HmSsAjlLIGcL6C4/z5Y4GeusMTlO7k0btDSfnXsTs3BmLFpq523+3/RKuTdRKFmAB7lne4KLd4XCu9yqOhQiucD3gYsuAgC8f3EMEU3g/IYwqqIqVtWGSospPhfyzqkPIxFScNGCCDRFwRWLuOhx8YIIYiEF59aHURNTsUIJFRfyqiP0ozu3IYxoSMElC/hYccXiKDRFwYXzw0iEqd5SF1cRCSnFhbyYxv368+eFEVGByxay73sXRRHWFFwwP4zKqIrVtaRxVkaU4kKeClItL5hHyucVixnrJQsjiGrA+fO4+LdK0jk9IeB4VKNZUx9GPEycqsSpKApxhhWc2xBGbYz02IhGjbzKCKfB5zWEEdVm4VSJs0LirJXT5mAhLyJxvmce1W4uW8S+ly2KIKJRuacqQpyzF/IAnr8L55PCW8S5IIJoiLHWSJzBQl5dTEV1VMWaelJeL54fgSJxqgpxx0Mc7zrpVBzSWNKaCHNBjjiBSxeWcIZUnu9EhHTd2qiKirBSXMgLqVS3uWA+1YveK/Pn0oURRDTMnXtyIe+ceuI8Vu6tmZ17AGqi9OE7tyFMnMGYLCrlXkVYJb28vp5bde/ahTzbJrHANIHXXgMAPNGZh+EKbBu0qJ82ZqMv46Iz6aJ5ysZI3sMeqX+2sY/UxOe7SENc32sgb1NDbrzg4ciEje6Ug54UPeLGCx52Dpko2ALre6lt9lynDtcX2NhnIi0psCM50i87kqRVHpC6Z9sGSYd9uZt9X+oiDXjLgImk4WP/qI3BLLXfWqcdDGU97Bu1kDJ9bOon5fOFTsa6rseA7pCmO1XwcGjcLmrOBbpuu4epZ7ehl5Ta5zt1+EJgQ6+BvEUNubG8h6ZJ4uxL03dtQvewfZCabet6GOvznTocT2BTv4m0SX24kZyH1ikH7dMOcUodu60D1Ip7qZuxvtxtwHB9bB2wMG14aByzqXGXdNAy5WA452HvqIWM6WNjPym8zwc4ew0UpP7dhO7h0ISN3pSD7pSDIxM2xvL0qMvbAhukBuDznTo8IfBan4ms7WPPsIVRibNL6uQdGqc+4PYhUlpfkThf6KRn4OYBE2k5JkM5D23TxDmYddE4Sjrz5n5q/70o8+eVbuOo3OuXudcyydzbOzv3Omfm3q6y3OtJU5fv8ISNiTly7/my3EuZPnDwIOtVcrmiktSptDetOEdRlC8KIX4g//9pAGkAlwevBe11FedYFjA0dPoV50B53UUr5cU5Ial1fjJFK8ZcxTllsZ7uxTknKlo5HYpz8DrG5G0rzlmwoEStPR2KcxRF+TiAq+T/LwcAIcR6AOng99fVDIMXu2EAv/gFAODftk2j4Pi4+3AOA1kPz3XoODhGh9MNvSwKebSFBSa37c/C8+kFBpA+mjZZkNKdouvr3hEWyrzczaKb+5vyyFg+btmbAQB8d0cari/wi8YsJgukarZNO3it18SOIROHxmw826ljKOfh7kPURf/xbvb94a4MTJcFGiN5Ul2PTNjYMmBic7+BlkkHT7YVMJZ38ctGFo18fydj/ckeEkXuPUIyz4udBhplAdK6XhNdSRcPt7Bg6Gf7San97g562v10XxYpw8NDzQV0JVmstHuYxScvdpFCfN+RPHIW/ecA4Hs70nA8gdsbsxjPs4imZcrBxj4D2wZNHBknyWg4R4qr4fr44S72/dGuDAzHx12HchjK0dX28LiNbYMmNvWxqOiJ1oIkLGXhlI3JzXsyyFqkFvelXbzUZWDfqIU9IxZe6THQk3LxYHMeKdPDrfuyENLDzhMCP9+fxbROSnPHtIP1vSZ2DZk4MGbjhU4d/Rl61eVtHzfKMfn+ThKbfnkgh9E86azNkw429xvYOmCiacLG0+06RnIu7jjA4qofyDH58e5MMfcGy3Jvx6CJ13rNIolrUvdwW+PM3Ltlb2Zm7kkS015JwOpJuXigiUVVs3PvtsYsxgou8PzzFNKYnqah6ym2N+VOLy/6vxFC/IGiKN8HsE4IsV6+PuNuf4Zwc/r0PRPr6df3HUG4URTlcnmB/418qRZAOdO/4XV/qGHQj7uuDvjyl4Fbb8Xn72/Bv3+oBrfuyeKPLqzA5gET59aHkbe5sn1ufRibBkz80QUVuGlPFt/4UC3+/tUknvgLEhj+9QO1uOtQDr91TgIHxiwsquQe91CWHm/Pdej4q/dW4Tvb6NP2+3c14abfqMc3t6bxf66sxuOtBVy3IoaulIOE3KttnXLwkVVxPNCUxz+8rxpf3ZTCQ38GfOaeJnzvo/X40c4M/uJS+qZdtjCCCbmivKxaw54RkoN+0ZjDV66lH91jfw786X3N+I8Pkazz6fMrsH3IwupaetklTR8XzQ9jXa+Bz15UiRt3ZfCtD9fh715J4rE/F/irh1rwL1fX4N4jefzG6jiaJhw0JLjX25emx9uTbTr+5+X03bv/c8Cn72rCjZ+ox7e3p/G3l1fjqfYCrllGYlFE7ncfmaDH272H8/inq6vxlddSePjz9Fz79ofr8JPdWXzukkqs6zFw0fwIknKnYFVtGDuGTPyP8yvw831ZfPW6WvzTq0k8/hf0+/vqB2ux9kAOv3duAntGLCyvppfdhO7hsoVRvNSl4/OXVuIHOzK4608EPn13E27+ZAP+Y3Ma//i+ajzYXMBHV8XQNuWgRu67dyVdXLciikdbSJr5+pY0Hvgc8Ad3N+FHH6/H97an8dfvJYHqqiVRDGU9uSev4cCYjU+dE8edB3P44jW1+NJrSTzyeeBP7m3CNz9ch1v3ZPHHF1ViU79xVO5tHqC/4C17svj6h2rx969Oz8i9Ow/l8DvnJNA4ZhVrFUbyHq5cLHPvMvrulefeN7ak8Z0PzsOy5x4HPvIREm5iMWDFilO7Zk/1Tq8oysflRf+YvNPfDuB2IUSjvNN/QgjxpeD9J3WnB7iIpygU0dA0uL7AmEOdtVCZKIEQoihk4PoCk+Njb7m4hELcZ0Q0fo1FNDRlZu69XpyLFy+GLyjkGeT0XD9XxWOUv66ro0p0NHpShQOn9EyvKMoX5vj3cfm3y+Wze3lLA6iX/68FMH3CCOdqsRgBLloEzJ+P0MIFWLZsGVatWI5ly5Zhpfy5fPlyrFi+vPg3raoBN+3hc9XXt6QB8NkzY/q461Ae3SkHL3Ya2DVsYfeIhec7dPSkHNx1iM/0P9zJ56pvbOVz1c17spjU6W/WOkWJrC0DJhpHLTzZpmMw6+L2Rj7Tf2c7j/ef29IwXYGf789hJEf/uEPjFIjY0Mvnx4dbChjP83nV9gS+uZV9v7+Dz/S/OphDf8bFs+069o3a2D5k4WXpv3bfEXq53bibz/Rf38Jn+h/vziBlUC6sM0mP+R1DJL8826GjN+3gjoP0kPt+GU7Ho4zVeIHrAc2TNtb3mtjcb+LgmIXH2+jhdlsjn+m/vY2xfnt7Gobj4xeNOQxl+Zx8YMzClgET63oonfVQM5/pb9nLZ/pvSJw/2Mln+jsO5tGbptzUnhEbO4ctvNhpoDPp4O7DfKb/8a4MhMTpCYGf7KaIyH1H8mifdvBKt4Ftgxb2j/K5vD/j4pcHKDv2vR3E+c2tfKb/6b4sxvL0mD8yYeO1PhMb+0wcHrfxWGsBozkXP9ufheVSWAQAvrudz/RrD+QwmHXxVJuO/aMWtg5aeKXbQOuUjQea8pjSvaNy74ezcu+FTgPtegLLly8v5vCq4/zE/Pm8BgLFnDehUuiU7vRylT5oXwbw1/L/Vwoh1iqK8kUA64UQjcGbPvnJT4qVK1cCAG644QbccMMNb/j4c7WhoaGSgGLBwyXnvEFxwq4hzK84WhjTCkQY1TJhzEBIMTie7DunMKbg3vdRwpiz+74eYcxZOI8njFkUjJx1vNcljHksnHMIYx4lGDkr1mnDQ23ZmIgynNljjElRGFPiPK4w5olw+kcLYx5zTGbhnEsYc8rwT5h7y5cuwpqzVr6peT+7vWWr90KIx4UQj4N39lr5WqM86McBpMsveABYuXIl1q5di7Vr177pFzwAJHW6j3o+KZgA8FyHjpzNPfGRvIf9YxSn7Jh2sG+Ue70b+03kbR/PdXB/9VFJkXyxizTWbQOkex4at9E8yT3+3cMWJgs+1vVyv/qpdh7vCUnNfKXHwLTuY+cwhR6bJrg3259xsX2Qe/gvdxtwPIHH2tj3mQ4dukM67rjc/+1KOWibcnBwzMZwzsOWARMZy8cLcn/+kVZSbF/opPvpZkmjbRyl4GNn0sHeEe7db+wzUbB9PCNxPiYpry93G0iaPrYPmhjIujg8QZy9ae6XT+k+Xu01YLkCT8hYn5RU23W9BiZ1H7uGTPSmHDRPOjg0wT377YOsR3ipm555wZg826GjYPvY1Ed68t5RC51JjkmjrBXYPGAia3FMhMTpSZwZ08eWARNDWdYRtE456Eo52DNiYSLv4bVeE7rj4+kAZxspzK/0GJg2fOwYMtGXcXFkwkbThIO+tIsdQyam/OFeCAAAD4BJREFUDB+v9hiwvBLOp9pJnV7fZ2Ci4GHPsIWeFGsRDo3bGMq62DZAGfAg9x45Tu41jZ66jPWptDelIk8IsRbA2lm/vy2tKqrhqiWsMvvQCgoIXr2UNMtLF0bQEFehKqyAUgA0xEnsuHRBBPEwaasA8KEVpEhetYR00YsWhDE/oSEepmdaWKWpQm1MxeWLoohqpIkCwAeXxxBRWQVWHVPxnnkR1MZIVw3MLkIqUB1VceXiCMKaguuWs+81y0jTvWxhBHVxVmtVSrMLy+M++cULIqiQsaoK6aKqouB9S6KoCLOya15CRVgNF80uamMS50JW7V2zjDivW0HK65WLI6iW1Wjz4hoqwgpURUE0pJAoInFGNOIDgGuXxRDVgMsXkab6nnkR1ERVNHiiaHahKvR6u2pxBKFZYxILc0zq4yrOrWdFoA9gXoJ050skzquXsuLw+hUxaApxV0SIMzD0CMwuqqMq6uKkv8ZCCj4Q4FxOCvOVi0mBvXB+pFj5B3BmEZWEmCsWRxFRy3AujyIaUvDehVHUxjScP4+YHL9kdnHRAqAyohZz7/pj5R7CWFl/YmHLt7KdnhV5p9BMV6Av7cIXpF4CQG/ahe0JDGVJZ50oeEibrCmf0D3kHYHhHN/Tl2Ztc1eSFMn+jAvLFRjJechZPqZ01oRnLB/jBQ+6Q2qn6wPdKR6vO+XAFcBAxoXpCIzlWVQ0bXiYMjxkLR+jeQ+my8/3fFJaAaAn5cLxgKGsC90pxZo0fUzqHvK2wHCOte59aRdCkLYphEBfxoXl8e95iTNp+kgHsdo8B47H4xRx+ozDdAVG8x5yNnFOy1jH8h4MR8yN0wcGsi50l+/LBDh11qaP5Mgh6M+48GaNieMBQzkXBYkzZfpIGT4mCx4KMlbbE+iVY9KZdOAL4rZc4szZPiaCMTF9jOc9FOSYOH4ZzhQpzAHOkZwrx9NDsjgmLgxXYCDjwhUojkl3irgHsy4Mp4QzafA85WzitMpyr/NYuad7mC44b/l1cLx2etben0LTFN5JFQAVEX6nJeRdKx5Si46zYZU16RGNd91YiFRS1ouzrwJIqihrwEOqImvRKXkV1RRoqoJ4OKhvD45HemUizMo9Hg/FKq6QxrunqvK9UIBK6WRaEVFKx1NIqQ0stDw/iDWw1GKslREViow9oMOGVD5rRjRSa8tjVRUep4hT2nOpalCDzrueKo0dYyGe13iIOIPzGvSNB7GGSjhVaaUVUHsTYXXGmFTIOOIh3qGjId6tffmMHFKB+OwxkeManNe4HJOoBjkmjCEkz0EwBgDPbxBr4MYb0nh+AwPLmDxX8TD7Bu6yFXJ8E2Gew5jE6WsAwBhiRZyMsXJW7sXKci/wp3+72rvvoleV4kVQHeXJrYqo8gLjAMUlPx0oJU6QhMFgVUflF0dYKRI5wvJiDan0TouHmbAVMklm9FX4ekgB4mEVYU1BVJbhRtQg+agMo8o+QazBF0hIZQKGNQWqLyBkoibCQV/irIqUEjtIvLBMxIgkosTlI0VFuDTlLsdZGVGK7yt+oSl044mH1CJOpaxvKVaeh+Ac+QBCPhDSGL+mKMULNsBZKaf+ibBavGgiGrfBfCHHRH4BlmIl3sqIWhoT2Tewqg6+8I6HM/iyDcsvGwXBeM7EOSN/wD6a/NINFoKDLzd+ESnFHCiOicy9inDpyyEaensn2O+66b3hUMHFE1R0AThNs11OT/M2p2dJk//GCh7yto8BOZUMpq5tUw58wemZ6QoMZTkFnCh4mNZ9pE0fIzlOwfszHlwfxSldR5LTwb6MC11OJTNyej5R4NRwOOfBcH30pjmVbJ9m384kVVv6My7yDqfbKdPHtMEpet6ieo8lY/WFQPs0p/fdaQemR5w5m+9PGnyMGctzyjyQceF4peln+7QDTwA96WDa6yFrk146ZXhIWz5G8i4MhzG5PtCRLMXq+kBfmudhJEclmCmd5ylrcQpuupyi+wIzx8RjPAU5JinDw7TB/+dsqsxYHh99hMTpC6reWHI8s7aP8YKPKYlzNO+hIGO1yx6bApx9aT5yDctYJwseJnWO7UiOOPsypHG3T8vHipQDx+fjmm5zTNJyTCYKjHUoS5w9aRc+SuPZPSv3xgseps5M79/cVh3TcPVSUhM/sorEhA8soy7cZQsjaEhonKLLb/gFCZIdLlsYQSJUWoz7yKo4NJWLRpVRBRcvCKM2pqEqwm/0kArURrmQd8Ui0kSvk4s3H1oRQ0QuGtXIRaOqCNVVfHC7Jx5WUS0XfsKqgutXMtZrl8cQD6l476II6mMqzm8IIx7itNfxuTh2iRoscHEB7yOrqCF3zdIYKsIKLl0QQX2CemwR+RjTECeNM1jgulYuUn14ZRwhlYuAVVEFF82PoDrGWZIKBWGNd7qaGBe4olppMe66FdSSu3JxFLUxFRfMi6AiQrIOFYKoDFMZVfC+pVzgKh+TeEjBexdF0BDXindBAWrkVUbkmEgdPUXiVBVqAFZEFFyyMIL6mFa8i2oKUBeXi6uLI4iH1CLO61fGuWC5pLSQVx1VUBejGk9E4528JkqdwLCm4PqVpYXZWEjB5YsiqI2reE8D6bmeT3JQIqwivABSC+/EubfizELem9sijooN3RYWhSN4skXSOLtMVCKMvUMOXEtF16SHqQwwlQU6Jjx4loo9gw6qEMYrndQge6pFx6JwBK91W4j7IRwcdmHoCnqnfYymBDJ5Bc1jLlRHw/Z+G3VqGC+0S1pum4EGLYytfRZCbghHRl3kCgqGUj4GpgX0gorDIw4ifgibey3MD0XwTKukq3YYqFbC2NVvQ9ga2sY9JHPAeEage9KHbajYP+SgQoSxodvEkghx+kJgfbeJShHGviEHjqmie9LHeEYgmQXaxz34tordAzaqlRLOp1t1LAhFsLnHQsQL4eCIA11XMTAtMJzykZU4NUfDtj4b9WoYz0ucL7QbqFfD2NZvQ3U0NI+5yOQVjCQF+qd86LqCgyMOYl4Im3osLAxF8JQck1c6TVQrYewedODZKjomPExngckM0D3pwzVV7B1yUIkw1nWZEELgyRYdi8MRbOg2EffDaBxyYZkKeqZ8jKcFUjmgbcwDbA07+23UKGG81MFYn2nVMT8UwZZeC2EvhCMjLgoFFYNJH0NJH7mCgqZRFyEvhK19FuZpYTzbxr4vdhioU8PYMWBDsTW0jrvI5BSMpgV6p3yYhoIDwy7ifuio3HtV5t6eQeZe56SH4Un7v+JSOGY7PXXvT6VNTpKhF4+zhn/ZstLvpsnKJscBNNY/w/OoPWZZrHia3ccwSn0jEb5fUfjPdfl5wXuO1deyeAyPyijQNGoGBMc7Xl/b5vuFoKjI7FhfL07TPP7xynEGsTrO68Pp+4z3ZHHGYqc2Jq5LDrCisG8kcuJYTxVnKESMJ4uzfEzmz6cL7VvY3nm696fSLAu4806a/d14I19bu5aD8+ST/FLYuhVoaQFaW4HNm0lXfOIJvvf22/nzJz+hJfDdd/Mzn38eGB4Gdu2iqEF3N91E02ngoYeYBD/9KfvecgsT6oEHqAvwyitAby/Q2Ajs3UsN85deYmLcey+T4qab2Pe225hEjz1GIZGNG4GODnqZ7dgBjI0BzzzDRL/jDnKsb7yRF9qvfsUkfvpp+gZs30414fZ2YNMmft7jj/PiuO02Hu+mm3j8e+5hYr74IhN1zx7gwAESn155hYzHBx8krltvZd+f/pSxPvQQz8O6dUBXF8/Prl38nOef5+fefTfP509+wr6/+AXH5IknOCabN3M8mps5PhMTHC/fL43fjTfyM+64gxfZs89SXGLnTuDwYTq7bthAnI88wth+/vMSzkgEuO++0pj09QH79vFfXx/w8sv82/338wK9+Wb2/dnP+KXyyCP87A0beKzDhzkmIyPAc88xprlyz/OIZXycGvYHD75Z2f6G2rvvTh/QcoMWjR792onaG+nzTux7Jta3r++bIHt1vPbO87I7lWZZ/BY+5xzeOd77Xt4lzzqLd+r583nXCk66ZZGnPDkJLF3KO9sll/Au95738M61YgW/pevqAF3nHSQUolhhfT0wOkraY2cncOml/CY/91zePZYu5Uyiqop3AiE4DcxkqIYyOAisXs278WWX8e5x9tl8feFC3kHjcd7xHId39ulpTg/7+0s4L7uMd/WzzuKdp6GBd61wmHcpw6CU8vg4vdC6u4nz4EHgvPOIe/ly3mFravj+QIo8l+PnjYxQr62jg8c7dAhYs4ZxLF7MuCorOQvxPMadThPHyeCMxXh+bJvna2qK56+3l1qJBw+WxmTlSp73+nqOQ4BT1zlOAc6urtKYBDiXLeN419SU2JwBznnzmCdnnVWKdTbOZJJ38wBnIkE26KJFM8fkWLlXUcEY3qb27rvTA6UL0/Pm/un7JbaSEEyWY713dh8hTq0vUPr/6+kbHO9k+vo+//524Xw9sR5vTAIc74YxKe/7JrHljtd+ve70AL95z7Qz7Uybs737FvLOtDPtTDtuO3PRn2ln2q9ZO3PRn2ln2q9ZO3PRn2ln2q9Ze1dd9M8999zbHcJJtzOxvjXtTKwnbmcu+repnYn1rWlnYj1xe1dd9GfamXamnbj9lxfnKIqyDkDvW/TxKwAMvEWf/Wa3M7G+Ne1MrGxnCSE+Mdcf/ssv+jPtTDvT3t72rpzeS7394P+fVhTl4+WvnWln2tvZ3u78fNeV4R7LQVdRlNXSkafxuB/wX9QURQnqos8ObL+OZ/H9drXTMaby9k45j0E7HfLzXXmnL2ufAQcfAHoAfPztC6XU5MCvl/4Aq+U3fTEB8EYtvt/kdjrGVN7eKefxOO1tyc931UU/h7deLU7VQfetaatRGuAe+fvp+AV1OsZU3t4p5xHA6ZOf77bpff3bHcDJtFkOQJcDeATAFTj9vqBqcfrFVGzvoPMYtNMiP99RF33Z81t565HPRG+dg+5b1OTUc5209X67w3nHtnfCeTyd8vMdddGfwCNvtaIoq8v+H3zzXxm8BmD2SX/L2vG+oMp+/3jZQlMap98XVBqnX0xztdP9PAKnUX6+oy764zXpnhtcbLXytUZFUa48loPuWxzPceWBFEX5QpCoMr637QvqOO10jGlGe4ecx9MqP88U57wNTQ7yY+CzZz2AP5CPKF+AXJB6O51/y9vpGFPQ3knn8XRqZy76M+1M+zVr76otuzPtTDvTTtzOXPRn2pn2a9bOXPRn2pn2a9bOXPRn2pn2a9bOXPRn2pn2a9bOXPRn2pn2a9bOXPRn2pn2a9bOXPRn2pn2a9b+fwhnWkfqb7fHAAAAAElFTkSuQmCC\n", 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from types import SimpleNamespace\n", "from matplotlib import pyplot\n", "from math import cos, sin, pi\n", "import numpy as np\n", "import scipy.stats as reg\n", "import kwant\n", "from sympy import S, Eq, solve, Symbol\n", "\n", "lat = kwant.lattice.square()\n", "\n", "s_0 = np.identity(2)\n", "s_z = np.array([[1, 0], [0, -1]])\n", "s_x = np.array([[0, 1], [1, 0]])\n", "s_y = np.array([[0, -1j], [1j, 0]])\n", "\n", "def HedgeHog(site,ps):\n", " x,y = site.pos\n", " r = ( x**2 + y**2 )**0.5\n", " theta = (np.pi/2)*(np.tanh((ps.r0 - r)/ps.delta) + 1)\n", " if r != 0:\n", " Ex = (x/r)*np.sin(theta)*s_x + (y/r)*np.sin(theta)*s_y + np.cos(theta)*s_z\n", " else:\n", " Ex = s_z\n", " return 4*s_0 + ps.Ex * Ex\n", " \n", "\n", "def Lead_Pot(site,ps):\n", " return 4*s_0 + ps.Ex * s_z\n", "\n", "def MakeSystem(ps, show = False):\n", " H = kwant.Builder()\n", "\n", " def shape_2DEG(pos):\n", " x,y = pos\n", " return ( (abs(x) < ps.L) and (abs(y) < ps.W) ) or ( \n", " (abs(x) < ps.W) and (abs(y) < ps.L))\n", " \n", " H[lat.shape(shape_2DEG,(0,0))] = HedgeHog\n", " H[lat.neighbors()] = -s_0\n", " \n", " # Leads\n", " sym_x = kwant.TranslationalSymmetry((-1,0))\n", " H_lead_x = kwant.Builder(sym_x)\n", " shape_x = lambda pos: abs(pos[1])